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Ïðåäëîæåíû íîâûå ïîäõîäû, àëãîðèòìû è èõ ïðîãðàììíàÿ ðåàëèçàöèÿ â îáëàñòè àâòîìàòè÷åñêîãî óïðàâëåíèÿ ñëîæíûìè ñèñòåìàìè, îðèãè- íàëüíûå èíôîðìàöèîííûå òåõíîëîãèè â íàóêå, îáðàçîâàíèè, ìåäèöè- íå. Äëÿ ïðåïîäàâàòåëåé óíèâåðñèòåòîâ, íàó÷íûõ ðàáîòíèêîâ, ñïåöèàëè- ñòîâ, àñïèðàíòîâ. Ó çá³ðíèêó íàâåäåíî ðåçóëüòàòè äîñë³äæåíü, ùî ñòîñóþòüñÿ êîìï ’ þ- òåðíî¿ ³íæåíåð³¿, óïðàâë³ííÿ, òåõí³÷íî¿ ä³àãíîñòèêè, àâòîìàòèçàö³¿ ïðî- åêòóâàííÿ, îïòèì³çîâàíîãî âèêîðèñòàííÿ êîìï ’ þòåðíèõ ìåðåæ ³ ñòâî- ðåííÿ ³íòåëåêòóàëüíèõ åêñïåðòíèõ ñèñòåì. Çàïðîïîíîâàíî íîâ³ ï³äõî- äè, àëãîðèòìè òà ¿õ ïðîãðàìíà ðåàë³çàö³ÿ â îáëàñò³ àâòîìàòè÷íîãî óïðàâë³ííÿ ñêëàäíèìè ñèñòåìàìè, îðèã³íàëüí³ ³íôîðìàö³éí³ òåõíîëî㳿 â íàóö³, îñâ³ò³, ìåäèöèí³. Äëÿ âèêëàäà÷³â óí³âåðñèòåò³â, íàóêîâö³â, ôàõ³âö³â, àñï³ðàíò³â. Ðåäàêöèîííàÿ êîëëåãèÿ: Â.Â. Ñåìåíåö, ä-ð òåõí. íàóê, ïðîô. (ãë. ðåä.), Ì.Ô. Áîíäàðåíêî, ä-ð òåõí. íàóê, ïðîô., È.Ä. Ãîðáåíêî, ä-ð òåõí. íàóê, ïðîô., Å.Ï. Ïóòÿòèí, ä-ð òåõí. íàóê, ïðîô., Â.Ï. Òàðàñåíêî, ä-ð òåõí. íàóê, ïðîô., Ã.È. Çàãàðèé, ä-ð òåõí. íàóê, ïðîô., À. Øòåôàí, äîêòîð-èíæåíåð, Ã.Ô. Êðèâóëÿ, ä-ð òåõí. íàóê, ïðîô., Î.Ã. Ðóäåíêî, ä-ð òåõí. íàóê, ïðîô., Í.Â. Àëèïîâ, ä-ð òåõí. íàóê, ïðîô., Å.Â. Áîäÿíñêèé, ä-ð òåõí. íàóê, ïðîô., Ý.Ã. Ïåòðîâ, ä-ð òåõí. íàóê, ïðîô., Â.Ô. Øîñòàê, ä-ð òåõí. íàóê, ïðîô., Â.Ì. Ëåâûêèí, ä-ð òåõí. íàóê, ïðîô., Â.È. Õàõàíîâ, ä-ð òåõí. íàóê, ïðîô. (îòâ. ðåä.). Àäðåñ ðåäàêöèîííîé êîëëåãèè: Óêðàèíà, 61166, Õàðüêîâ, ïðîñï. 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Îòìåòèâ, ÷òî E( A ) äëÿ ëþáîãî êîíå÷íîãî àâòîìàòà A åñòü ïîäìíî- æåñòâî Z * , âûäåëèì äîïîëíèòåëüíî íåñêîëüêî ñïåöèôè÷åñêèõ ïîäìíî- æåñòâ ýòîãî ìíîæåñòâà:  – ïóñòîå ìíîæåñòâî ñëîâ (ïóñòîå ñîáûòèå);  – ìíîæåñòâî ñëîâ íóëåâîé äëèíû (åäèíè÷íîå ñîáûòèå); {z i } – ìíîæå- ñòâî ñëîâ, åäèíñòâåííûì ýëåìåíòîì êîòîðîãî ÿâëÿåòñÿ z i  Z; i=1,2,…...,n (ýëåìåíòàðíûå ñîáûòèÿ). Êðîìå òåîðåòèêî-ìíîæåñòâåííûõ îïåðàöèé íàä ñîáûòèÿìè, îïðåäå- ëÿþò è ðÿä äîïîëíèòåëüíûõ îïåðàöèé, ñðåäè êîòîðûõ âûäåëÿþò: – êîíêàòåíàöèþ ñîáûòèé P è Q: R= Q P  = {r  Z * q p r |   , p  P, q  Q}, – èòåðàöèþ ñîáûòèÿ P: (P) * = ... P P     , – ëåâîå ÷àñòíîå P íà Q: R=P\Q={r  Z * |  p  P, Q r p   }. Îòìåòèì, ÷òî îïåðàöèè îáúåäèíåíèÿ, êîíêàòåíàöèè è èòåðàöèè ñîáûòèé ïîëó÷èëè íàçâàíèå îïåðàöèé íàä ðåãóëÿðíûìè ñîáûòèÿìè, ïîä êîòîðûìè ïîíèìàþòñÿ êîíå÷íûå ñîáûòèÿ èëè ñîáûòèÿ, îáðàçîâàí- íûå èç êîíå÷íûõ ñ ïîìîùüþ êîíå÷íîãî ïðèìåíåíèÿ ïåðå÷èñëåííûõ îïåðàöèé. Âçàèìîñâÿçü ìåæäó ñîáûòèÿìè è êîíå÷íûìè àâòîìàòàìè âïåðâûå ïîêàçàíà Ñ.Ê.Êëèíè. Äîêàçàííóþ â [2] îñíîâíóþ òåîðåìó ìîæíî ïðîèíòåðïðåòèðîâàòü ñëåäóþùèì îáðàçîì: ðåãóëÿðíûå ñîáûòèÿ è òîëüêî îíè ðàñïîçíàþòñÿ êîíå÷íûì àâòîìàòîì. Äðóãèìè ñëîâàìè, åñëè ñóùåñòâóåò êîíå÷íûé àâòîìàò A , òî ðàñïîçíàâàåìîå ýòèì àâòîìà- òîì ñîáûòèå E( A ) ðåãóëÿðíî, è îáðàòíî, – åñëè P – ðåãóëÿðíîå ñîáûòèå, òî ñóùåñòâóåò êîíå÷íûé àâòîìàò A , ðàñïîçíàþùèé ýòî ñîáûòèå, ò.å. E( A )=P. Òåîðåìà Êëèíè ÿâëÿåòñÿ îñíîâîïîëàãàþùèì óòâåðæäåíèåì, èñïîëü- çóåìûì êàê òåîðåòèêàìè, òàê è ïðàêòèêàìè, ïðèìåíÿþùèìè êîíå÷íî- àâòîìàòíóþ ìîäåëü äëÿ ðåøåíèÿ ðàçëè÷íûõ âîïðîñîâ, ñâÿçàííûõ ñ èññëåäîâàíèåì è ïðîåêòèðîâàíèåì óñòðîéñòâ è ñèñòåì ïîñëåäîâàòåëü- íîñòíîãî äåéñòâèÿ. Ïåðâûì è îñíîâíûì òåîðåòè÷åñêèì âûâîäîì, ñëå- äóþùèì èç òåîðåìû Êëèíè, ÿâëÿåòñÿ óòâåðæäåíèå òîãî ôàêòà, ÷òî ìíîæåñòâî âñåõ ðåãóëÿðíûõ ñîáûòèé çàìêíóòî îòíîñèòåëüíî òðåõ îïå- ðàöèé Êëèíè, ò.å. ìíîæåñòâî âñåõ ðåãóëÿðíûõ ñîáûòèé ñ îïðåäåëåííû- ìè íà íåì îïåðàöèÿìè îáúåäèíåíèÿ, êîíêàòåíàöèè è èòåðàöèè ñîáû- òèé ïðåäñòàâëÿåò ñîáîé çàìêíóòóþ àáñòðàêòíóþ àëãåáðó, àêñèîìàòè÷åñ- êàÿ ñèñòåìà êîòîðîé âêëþ÷àåò êîíå÷íîå ÷èñëî òîæäåñòâ-àêñèîì:      ; o"xklUlmi ! 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Äîêàçàòåëüñòâî ïîëíîòû ïðèâåäåííîé âûøå àêñèîìàòè÷åñêîé ñèñòå- ìû ìîæíî íàéòè â [3] . Íàèáîëåå èíòåðåñíûì ýëåìåíòîì ýòîé ñèñòåìû ÿâëÿåòñÿ ñïåöèàëüíîå ïðàâèëî âûâîäà, êîòîðîå, âî-ïåðâûõ, ïîçâîëÿåò îãðàíè÷èòüñÿ êîíå÷íûì ìíîæåñòâîì òîæäåñòâ è, âî-âòîðûõ, ñîâìåñòíî ñ ýòèìè òîæäåñòâàìè ÿâëÿåò ñîáîé ýôôåêòèâíûé èíñòðóìåíò âûâîäà è äîêàçàòåëüñòâà ðàâåíñòâ â àëãåáðå ðåãóëÿðíûõ ñîáûòèé. Íàèáîëåå öåííûì ïðàêòè÷åñêèì ñâîéñòâîì àëãåáðû Êëèíè ÿâëÿåòñÿ âîçìîæíîñòü áûòü îïèñàííîé ïîñðåäñòâîì ðåãóëÿðíûõ âûðàæåíèé. Ïîëàãàÿ, ÷òî Z= {z 1 ,…,z n } åñòü ïîðîæäàþùåå ìíîæåñòâî àëãåáðû Êëèíè, à  ,  , *,  , (, ) – ñèìâîëû, ñëóæàùèå äëÿ èíäèâèäóàëüíîãî îïèñàíèÿ ëþáîãî ýëåìåíòà àëãåáðû è íå ïðèíàäëåæàùèå Z, òî â ñîîòâåòñòâèè ñ [4] ðåãóëÿðíîìó âûðàæåíèþ ìîæíî äàòü ñëåäóþùåå êîíñòðóêòèâíîå îïðåäåëåíèå: 1) êàæäûé ñèìâîë  ,  , z 1 ,… ..., z n åñòü ðåãóëÿðíîå âûðàæåíèå; 2) åñëè  è  – ðåãóëÿðíûå âûðàæåíèÿ, òî òàêîâûìè æå ÿâëÿþò- ñÿ    ,    , (  )*; 3) íèêàêàÿ ïîñëåäîâàòåëüíîñòü íå ÿâëÿåòñÿ ðåãóëÿðíûì âûðàæåíè- åì, åñëè îíà íå îáðàçîâàíà êîíå÷íûì ïðèìåíåíèåì ï. 1 è 2 íàñòîÿùåãî îïðåäåëåíèÿ. Ïåðåõîäÿ ê ïðèêëàäíûì àñïåêòàì êîíå÷íîàâòîìàòíîé ìîäåëè, îáû÷íî ïðåäïîëàãàþò åå èñïîëüçîâàíèå ïðè ïðîåêòèðîâàíèè ïîñëåäîâàòåëüíîñ- òíûõ ìàøèí íà îñíîâå çàäàííîãî èõ ïîâåäåíèÿ. Ïðè ýòîì ïîä ïðîåêòè- ðîâàíèåì ïîíèìàþò ñîâîêóïíîñòü ïðîöåäóð ñèíòåçà è àíàëèçà, îáúåäè- íåííûõ îáùèì êðèòåðèåì êà÷åñòâà. Ïîñëåäíèé â áîëüøèíñòâå ñëó÷àåâ íîñèò ýêîíîìè÷åñêèé õàðàêòåð è ïðåäïîëàãàåò ìèíèìèçàöèþ ëèáî ÷èñëà ñîñòîÿíèé ïðîåêòèðóåìîãî àâòîìàòà, ëèáî âðåìåíè ïðîåêòèðîâà- íèÿ. Àáñòðàêòíûé ñèíòåç àâòîìàòà ïðåäñòàâëÿåò ñîáîé ïðîáëåìó, ñâÿçàí- íóþ ñ ïðåîáðàçîâàíèåì îïèñàíèÿ ïîâåäåíèÿ àâòîìàòà â òåðìèíàõ ÿçûêà ðåãóëÿðíûõ âûðàæåíèé â êàêóþ-ëèáî ôîðìó ïðåäñòàâëåíèÿ ôóíêöèè ïåðåõîäîâ  ýòîãî àâòîìàòà. Ðàññìàòðèâàÿ êîíêðåòíûå ïðîöåäóðû ñèíòåçà, îáðàòèì âíèìàíèå íà òîò ôàêò, ÷òî ëþáîå ñëîâî p  E( A ) , ïîäàííîå íà âõîä àâòîìàòà, ïåðåâîäèò åãî èç íà÷àëüíîãî ñîñòîÿíèÿ a 0 â íåêîòîðîå êîíå÷íîå ñîñòîÿíèå f  F. 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Äðóãèìè ñëîâàìè, åñëè q – ñëîâî, ïîäàííîå íà âõîä àâòîìàòà â ñîñòîÿíèè a 0 è ïåðåâîäÿ- ùåå ýòîò àâòîìàò â ñîñòîÿíèå a i , ò.å. a i =  (a 0, q), òî Ea i ( A )=q\E( A ) è Ea i ( A ) åñòü ëåâîå ÷àñòíîå E( A ). Âû÷èñëÿÿ ëåâûå ÷àñòíûå ñîáûòèÿ è îòîæäåñòâëÿÿ èõ ñ ñîñòîÿíèÿìè àâòîìàòà, ìîæíî îïèñàòü åãî ïîâåäå- íèå, ò.å. îïðåäåëèòü, ïîä âîçäåéñòâèåì êàêèõ ñëîâ àâòîìàò ïåðåõîäèò â òî èëè èíîå ñîñòîÿíèå. Ïðèíÿâ âî âíèìàíèå êîíå÷íîñòü ìíîæåñòâ A è Z , ïðèõîäèì ê çàêëþ÷åíèþ, ÷òî ÷èñëî ðàçëè÷íûõ ÷àñòíûõ ñîáûòèé äëÿ E( A ) êîíå÷íî. ×òîáû îò ÿçûêà ñîáûòèé ïåðåéòè ê ÿçûêó ðåãóëÿðíûõ âûðàæåíèé, â [4] ïðåäëîæåíî ïîíÿòèå “ ïðîèçâîäíàÿ îò ðåãóëÿðíîãî âûðàæåíèÿ ” , êîòîðîå îïðåäåëåíî ñëåäóþùèì îáðàçîì: 1. D  (  )=  ; 2. Dz i (z i )=  ; 3. Dz i (  )= Dz i (z j )=  ; (i  j); Dz i (    )=Dz i (  )  Dz i (  ), Dz i (  .  )=(Dz i (  )) .    (  ) . Dz i (  ), Dz i ((  ) * )=(Dz i (  )) . (  ) * ; 4. Dp(  )=Dz i . (Dq(  )); p=q.z i ; p,q  Z * ; z i  Z. Çäåñü  è  – ðåãóëÿðíûå âûðàæåíèÿ;  (  ) – ñïåöèàëüíûé îïåðàòîð, ðàñïîçíàþùèé ïðèíàäëåæíîñòü  ê  . Îí îïðåäåëÿåòñÿ òàêæå ðåêóðñèâíî: 1.  (  )=  (z i )=  ; i=1,2,… ... ,n,  (  )=  . 2.  (    )=  (  )   (  ),  (  .  )=  (  )   (  ),  ((  ) * )=  . Àíàëèç ïðèâåäåííûõ îïðåäåëåíèé ïîêàçûâàåò, ÷òî: 1) Dz i (  )=z i \E(  ), ò.å. ïðîèçâîäíàÿ ðåãóëÿðíîãî âûðàæåíèÿ  ïî ïåðåìåííîé z i  Z îáîçíà÷àåò ëåâîå ÷àñòíîå ñîáûòèå E(  ) îòíîñèòåëüíî ýëåìåíòàðíîãî ñîáûòèÿ z i ; 2) Dz i (  ), ãäå  –ïðîèçâîëüíîå âûðàæåíèå â àëôàâèòå Z ,åñòü ðåãó- ëÿðíîå âûðàæåíèå â ýòîì æå àëôàâèòå; 3) Dp(  ), ãäå p – ïðîèçâîëüíàÿ ïîñëåäîâàòåëüíîñòü áóêâ àëôàâèòà Z, âêëþ÷àÿ  , åñòü ðåãóëÿðíîå âûðàæåíèå; 4) p E  (  ), åñëè è òîëüêî åñëè   Dp(  ); 5) äëÿ ëþáîãî ðåãóëÿðíîãî âûðàæåíèÿ ñóùåñòâóåò êîíå÷íîå ìíîæå- ñòâî S={D0,D1,D2,…} ïîïàðíî íå ýêâèâàëåíòíûõ (õàðàêòåðèñòè÷åñêèõ) ïðîèçâîäíûõ (çäåñü Di–ïîäìíîæåñòâî õàðàêòåðèñòè÷åñêèõ ïðîèçâîä- íûõ  ïî ïîñëåäîâàòåëüíîñòÿì äëèíû i); )xm\etwgv˶ݝ.[bI[-C ~PQ# bV %OXI@VE R]IH}c 7s󜝻Y&~4gs^s=OѬ^3["hpGDMf87;ְp-eo:Rt9Hxgо9{>2uVA_ T[ ӳxo S|zlt8_;vll]xA{ ]w%zt_gL>uWcv3Mlֳ0BŶlu;ޔ]E|^ԯۛ!ntzHOZ3`^w^}6?29Am;>>_:E1j*ګ1T7b[nBþqHo%Pi~/:~}ԊKS~)k}5կbbcJc\~x{ PnrٞޅOխPx`}'\}3z^Q>^@~BʜaU3!Pcdm6 K5 S,!]ē♨Tȣzg\LۅG{kfizvEi-)]o=aiW|u2{MF_XOOl]؃s깽({om U N;GAklr~[;x"cy:N:d࿖S${o [/_ ^þ}q􏀇&B6<=\ ,tS[מJU:3QGwghk^Y;mZ3Πy+~drȮ|^?Q{C |'+U)lUp'{]Atk7 q ߅O p ?= Qv x"p/z>Zg~\Q(jz휗0S]z&uw?Ň8gk[H]|;vN# >;|=rswm9:=DZ=d3c),9H?O|}s#~^|t]YY.w)ٜ,SqU_߯V _{=O^V&{u/#yy;gM^hm}tV?nm2^v/Y_OzZ|_#Ǚiݎ/_u2@' t2i:dN:e_S3  FN  BLNTN(16\N2N/ N1M\\{`x ]Uw0#Đ[bB&a4/#F(\4!mh D jiD5-Y}tcGAQF@ EP$!T@wڵsOթTrj{ߓGDWEBbTip{Ch K64OTuh_/>ʬ:A?}8\ ׄCE4,_e^UbQUR2_]!EWI}?[VN_5:+\Q"S!LYP['3Gޏ\^!/afeU?mZµb$H?S%3Yi/:2<0mm}ߩ+C82֣7Gm¤!kL}SZκxYWfqG. .aNiγ4G\}Yg|s/N~\rR9z3\!F}]~ErUv[fmxKߩm[|AWܐ91+ƥGGz ~z%/Cy S$C_yc8۩$s:cz7._/14.?uqIt\qIewdc+S9/M3.q̉zy[W?K5pXNS=.7FѸC%l /9 O?G?J^)blүDܶvKEoL?]r%SyUҔd$ޚ*Y FAr3^t+l-_6;t_+gvЗ\BQtqE "mQkۦLhFݼN0~ #~+;n`yNUQO_Rv#ny+5[2M180zDCy<<^oWWWoP_Ww |q$*¢Պ( W+q5 gq?jv\E="Ak=S>ßuC:bn3n[:j\pyudܸj1.aM;-00=n \])]<ļ(*a{تعj{,v+LSmZ/K;|/e@EJqP,{'fmn ]˜1DRG [m-!n=7jŽ;xۯ$_q) n1GTKG'Å ߤ}Oke16ȍwyT6Tkal&4Ԡ6c7ز{-w0W`KiGX25rS%eq*{W~츊c vwl]?ƥ4l\E#, Wo*qjOs08x;8Ige'l[oCvz[{lTxM0EdQ WTR<*_$#<&y2Ogi¦Sr8&HOwZ@|!7s;,srV.|"~u'y)x\6vִ-jaM5Lx^7 fw~O&nyGƥߡc\JövƗk-X cc)K?-s߱?~I5ebk-NrHWQi"ZrRrŪك*^j VZ:u!3{+?cX'UZ`WϬ Kz{պ. 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']OQ9XYi6z!AB D3AY䭈Xw\k5ka'%]{} d2%:mc=8r\&u\O~ݐ4u7=>h;4- BoKo/ؿNtګԶJ^Ww{COj3}li+~M_۸'iW͎H1CzFW{7\`oOYU YkdS8_ԾL+_AСXqkҩLЅJs\iv{ yD?Cud|M&z_ 5cC *>|Ynh \2Sr>Wf=?>!Msu2.i_+0HEd U2ҾG_]ɭA&9+9:a]c]a q}Puv/{fif݆:Dԡ~ͯIN˺Ck7-U~kPkKkKgNk1.a8GZه pgg7ŏqvWl~]CEq8ɺ ${j쥱oUr)wlP6xۑݧؘˠNQ/{ޥJ.Uldr^8zۭӔ{$ }]m6E;5*}N;6(̎O7N!js%ܗx2Edֻ^- Z=qAϺ~eXȕ^o)sNti^]+C{nїTHOD_y❩Ez@qɶLkrHe< hD\$jh,p޲^p5lQ}>Sa ϲƏYe~9i8#Q.tē*.m!L΂i7m(amv%utzx[%[' WNʸ3ΨhmǏ q7]g[e^\,\oqx"Lew5nJr+SŒp;-n] wf܅=]ɓwL26"~h!Od-udk;WS2SZy+MQ:*ľ|P5ײOnVwwZ;ЫZ龀^ =VtgDEㄱZ SJtj;KvݴcNƠ\l+a@Pc?!oW\Ƭ݈R%~P6b1OM.CVa}Ke`?Oܣ❡EQesuM=;7ȿ!vF7nVW[76M^nQ>v&60}ÅfK09Ǹ~f& WGēw-\ؾ: '-#s~\\䫈-(bv%^P\ֵ.{⽹"qpo Ti)v@zڭ4L[7< N&dw'C͏ >`y8'AK\{5L”G~<ěOY.m lN~tԝݢmslM \b .^^7a7՟bg K[qvTo~3Qdz}~)uB!;@'=q9'-9 qO<#Wt]FZ e2IG9֟I3lu].Mqio4/0OJHMHbi]ټ7POd؈^y7)qٗa#5p>"K },K✖yQIK~2/ݘG8nu8-.e36H[tFWEg댸{3־x7}t|-2߷˯ap_{vۮrVk1vq'+"tY9Ysw>␩I㱀xaEDG_ңG..jz+" enoE<-ZۦϪ@w\jsHNVq0-ͼc +:b%8Ȭ82GС_;h:Ϩaɔl,7끴[W׺!-OZ΃IO>R/72R <&h㾹_cʈ.wk.wwxEd.לh`p0̮l=Yu)<#MvkeNi{r@F!K\M?ḓ#,[+0Q4Iǘ%t4?Ǔa>aڄN\q׌n!o4鴅g<,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:447 6) åñëè Dp(  )  S, òî Dp  zi(  )  S, ò.å. åñëè ñðåäè ïðîèçâîäíûõ ïî ïîñëåäîâàòåëüíîñòÿì äëèíû k íå îáíàðóæåíî íè îäíîé õàðàêòåðèñòè- ÷åñêîé ïðîèçâîäíîé, òî òàêîâûå íå îáíàðóæàòñÿ è ñðåäè ïðîèçâîä- íûõ  ïî ïîñëåäîâàòåëüíîñòÿì äëèíû k+1. Ñëåäóÿ óòâåðæäåíèÿì, ïðèâåäåííûì âûøå, ëåãêî ïîñòðîèòü àëãî- ðèòì àáñòðàêòíîãî ñèíòåçà êîíå÷íîãî àâòîìàòà A , ïîâåäåíèå êîòîðîãî ñïåöèôèöèðîâàíî ðåãóëÿðíûì âûðàæåíèåì  â àëôàâèòå Z. Îñíîâíàÿ òðóäíîñòü ðåàëèçàöèè òàêîãî àëãîðèòìà çàêëþ÷àåòñÿ â óñòàíîâëåíèè ýêâèâàëåíòíîñòè âû÷èñëÿåìûõ ïðîèçâîäíûõ. Íàèáîëåå åñòåñòâåííûì ÿâëÿåòñÿ ìåòîä âçàèìíûõ ïðåîáðàçîâàíèé ñðàâíèâàåìûõ íà ýêâèâàëåí- òíîñòü ðåãóëÿðíûõ âûðàæåíèé. Íåäîñòàòîê ìåòîäà ñîñòîèò â òîì, ÷òî òðåáóåò îò èñïîëíèòåëÿ îïðåäåëåííûõ ìàòåìàòè÷åñêèõ íàâûêîâ è îïè- ðàåòñÿ ïðåæäå âñåãî íà èíòóèöèþ. Çàäà÷åé àáñòðàêòíîãî àíàëèçà êîíå÷íîãî àâòîìàòà ÿâëÿåòñÿ ïîñòðîå- íèå ðåãóëÿðíîãî âûðàæåíèÿ, ïðåäñòàâëÿþùåãî ñîáûòèå, ðàñïîçíàâàå- ìîå ýòèì àâòîìàòîì, ïî îïèñàíèþ åãî ïîâåäåíèÿ. Äëÿ êàæäîãî ñïîñîáà çàäàíèÿ ïîâåäåíèÿ àâòîìàòà (òàáëèöà ïåðåõîäîâ, äèàãðàììà ñîñòîÿíèé, ñèñòåìà õàðàêòåðèñòè÷åñêèõ óðàâíåíèé, ñïèñêè ïåðåõîäîâ) ìîæíî ïðè- âåñòè ñâîþ ïðîöåäóðó àíàëèçà. Êëàññè÷åñêîé ÿâëÿåòñÿ ïðîöåäóðà ðåøå- íèÿ ñèñòåìû õàðàêòåðèñòè÷åñêèõ óðàâíåíèé, ïðåäñòàâëÿþùåé àíàëèçè- ðóåìûé àâòîìàò [4]. Èñõîäíûì çàäàíèåì àâòîìàòà ÿâëÿåòñÿ ñèñòåìà óðàâíåíèé âèäà:  s1 =  s1   11 0   s2   21 0  …...   sn   n1 0 ,  s2 =  s1   12 0   s2   22 0  …...   sn   n2 0 , ..............................................................  ss =  s1   1s 0   s2   2s 0  ... …   sn   ns 0   , .................................................................  sm =  s1   1m 0   s2   2m 0  …   sn   nm 0 , ãäå s – íîìåð íà÷àëüíîãî ñîñòîÿíèÿ àâòîìàòà a 0 ; m – êîëè÷åñòâî ñîñòîÿíèé àâòîìàòà;  kl – èäåíòèôèêàòîð ñîáûòèÿ, ïðåäñòàâëÿþùåãî ìíîæåñòâî âõîäíûõ ïîñëåäîâàòåëüíîñòåé, ïåðåâîäÿùèõ àâòîìàò èç ñî- ñòîÿíèÿ k â ñîñòîÿíèå l;  kl 0 = z i , åñëè  (a k ,z i )=a l , è  – â ïðîòèâíîì ñëó÷àå. Ðåøàåòñÿ ñèñòåìà ìåòîäîì ïîäñòàíîâêè. Îêîí÷àòåëüíî ñîáûòèå, ðàñïîçíàâàåìîå àíàëèçèðóåìûì àâòîìàòîì, ïðåäñòàâëÿåòñÿ ðåãóëÿðíûì âûðàæåíèåì sf f r      . Ñóùåñòâóåò è ðÿä äðóãèõ ìåòîäîâ àíàëèçà è ñèíòåçà àáñòðàêòíûõ àâòîìàòîâ, íî îíè íå îáëàäàþò óíèâåðñàëüíîñòüþ ðàññìîòðåííûõ ìåòî- äîâ è, êàê ïðàâèëî, íàïðàâëåíû íà áîëåå óçêèé êëàññ ñîáûòèé. Ïðîòîêîëû óïðàâëåíèÿ âçàèìîäåéñòâèåì îáúåêòîâ ðàñïðåäåëåííîé ñèñòåìû ìîäåëèðóþòñÿ ïðîòîêîëüíûìè àâòîìàòàìè ÏAi(i=1,N), êàæ- äûé èç êîòîðûõ ïðåäñòàâëÿåò àâòîìàò ñ îäíèì íà÷àëüíûì è ôèêñèðî- âàííûì ìíîæåñòâîì êîíå÷íûõ ñîñòîÿíèé. 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Áóêâà z k âõîäíîãî àëôàâèòà Z îáîçíà÷àåò ýëåìåíòàðíîå ñîáûòèå, íàñòóïëåíèå êîòîðîãî ñòàíîâèòñÿ âîçìîæíûì òîëüêî ïðè èñòèííîñòè íàáîðà óñëîâèé EC k , ò.å. EC k =1 îïðåäåëÿåò âîçìîæíîñòü ïåðåõîäà ÏA i â î÷åðåäíîå ñîñòîÿ- íèå. Ïðè÷èíîé ïåðåõîäà i-ãî ïðîòîêîëüíîãî àâòîìàòà èç îäíîãî ñîñòîÿ- íèÿ â äðóãîå ÿâëÿåòñÿ ëèáî ïðèåì ñîîáùåíèÿ îò ÏA j (j  i), ëèáî ïîñûë- êà ñîîáùåíèÿ j-ìó ÏÀ, ëèáî ðåçóëüòàò íåêîòîðûõ âíóòðåííèõ äåé- ñòâèé, íå ñâÿçàííûõ ñ ïîñûëêîé èëè ïðèåìîì ñîîáùåíèé (íàïðèìåð, òàéìàóò). Íàõîäÿñü â êîíêðåòíîì ñîñòîÿíèè, ÏÀ i îáÿçàí âûïîëíèòü ñïèñîê äåéñòâèé LA k (k-þ ïðîöåäóðó), ÷òî, â ñâîþ î÷åðåäü, ìîæåò áûòü îäíîé èç ïðè÷èí íàñòóïëåíèÿ ñëåäóþùåãî ñîáûòèÿ. Ïåðåõîä â îäíî èç êîíå÷íûõ ñîñòîÿíèé ñâèäåòåëüñòâóåò î âûïîëíåíèè ïðîòîêîëüíûì àâòîìàòîì êàêîé-ëèáî óñëóãè èç ïðåäîñòàâëÿåìîãî ñåðâèñà. Èç ñêàçàííîãî âûøå ñëåäóåò, ÷òî ÏÀ â ÷èñòîì âèäå íå ÿâëÿåòñÿ êîíå÷íûì àâòîìàòîì. Îäíàêî åñëè êàæäîé âûïîëíÿåìîé ÏÀ ïðîöåäóðå (LA k ) ñîïîñòàâèòü âíóòðåííåå ñîñòîÿíèå àâòîìàòà, à ôóíêöèþ ïåðåõî- äîâ  ïðè ýòîì îïðåäåëèòü íà ìíîæåñòâå âûäåëåííûõ ïðîöåäóð (àëãî- ðèòìîâ âûïîëíåíèÿ LA k ), òî ÏÀ i â òàêîé èíòåðïðåòàöèè, áåçóñëîâíî, ìîæåò áûòü âîñïðèíÿò êàê ðàññìîòðåííàÿ ìîäåëü êîíå÷íîãî àâòîìàòà ñî âñåìè âûòåêàþùèìè ïîñëåäñòâèÿìè. À ýòî çíà÷èò, ÷òî âñå áåç èñêëþ÷åíèÿ ìåòîäû ïðåîáðàçîâàíèÿ, àíàëèçà è ñèíòåçà êîíå÷íûõ àâòî- ìàòîâ ìîãóò áûòü ïðèìåíåíû è äëÿ ïðîòîêîëüíûõ àâòîìàòîâ. Ñàì æå ÏÀ ìîæåò áûòü çàäàí íà ëþáîì èç àâòîìàòíûõ ÿçûêîâ. Èñïîëüçîâàíèå ÿçûêà ðåãóëÿðíûõ âûðàæåíèé äëÿ ñïåöèôèêàöèè ÏÀ ïîçâîëÿåò, âî-ïåðâûõ, ïîëó÷èòü äîâîëüíî êîìïàêòíûå îïèñàíèÿ è, âî-âòîðûõ, îðãàíèçîâàòü àâòîìàòè÷åñêîå ïðîâåäåíèå òàêèõ ïðîöåäóð ïðîåêòèðîâàíèÿ ïðîòîêîëîâ êàê ëîãè÷åñêîå ïðîåêòèðîâàíèå, óñòàíîâ- ëåíèå ëîãè÷åñêîé êîððåêòíîñòè, ìîäåëèðîâàíèå, äåêîìïîçèöèÿ è, íà- êîíåö, ðåàëèçàöèÿ. Ïîëó÷åííûå íà ýòàïå ñïåöèôèêàöèè ðåãóëÿðíûå âûðàæåíèÿ R 1 ,…,R N , îïðåäåëÿþùèå ïîâåäåíèå ïðîòîêîëüíûõ àâòîìàòîâ ÏÀ 1, …,ÏÀ N , ÿâëÿþòñÿ èñõîäíûì ìàòåðèàëîì äëÿ ïðîöåäóðû àëãåáðàè÷åñêîé âåðèôèêàöèè. Èñïîëüçóÿ àêñèîìàòè÷åñêóþ ñèñòåìó àëãåáðû ðåãóëÿðíûõ ñîáûòèé, ðàñøèðåííóþ ðÿäîì òîæäåñòâåííûõ ïðåîáðàçîâàíèé, ðåãëàìåíòèðóþ- ùèõ âçàèìîäåéñòâèå ïðîöåññîâ, ìîæíî ïðåäëîæèòü ýôôåêòèâíóþ ïðî- öåäóðó óñòàíîâëåíèÿ ëîãè÷åñêîé êîððåêòíîñòè (ïîëíîòà è íåïðîòèâî- ðå÷èâîñòü) ïåðâè÷íîé ñïåöèôèêàöèè àíàëèçèðóåìîãî ïðîòîêîëà. Ýòàï ëîãè÷åñêîãî ïðîåêòèðîâàíèÿ ïðîòîêîëîâ áàçèðóåòñÿ íà èñ- ïîëüçîâàíèè àëãîðèòìà àáñòðàêòíîãî ñèíòåçà êîíå÷íîãî àâòîìàòà. Ðå- çóëüòàò ýòîãî ýòàïà ïðîåêòèðîâàíèÿ ÏÀ (òàáëèöà ïåðåõîäîâ) ñ óñïåõîì ìîæåò áûòü èñïîëüçîâàí äëÿ ïðîâåäåíèÿ âåðèôèêàöèè ïðîòîêîëà ìåòî- äîì àíàëèçà äîñòèæèìûõ ñîñòîÿíèé. 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Ýòî è ôóíêöèîíàëüíàÿ ïîëíîòà, è íåïðîòèâîðå÷èâîñòü, è îòñóòñòâèå íåñïåöèôèöèðîâàííûõ ïðèåìîâ, ñòà- òè÷åñêèõ è äèíàìè÷åñêèõ òóïèêîâ è, íàêîíåö, âûïîëíåíèå íàçíà÷åíèÿ ïðîòîêîëà. Âîçíèêàþùàÿ ïðè ðåàëèçàöèè ìåòîäà àíàëèçà äîñòèæèìûõ ñîñòîÿíèé ïðîáëåìà ðàçìåðíîñòè ìîæåò áûòü ñâåäåíà ê çàäà÷å äåêîìïî- çèöèè êîíå÷íîãî àâòîìàòà. Ýòàï ðåàëèçàöèè ïðîòîêîëîâ â òîé èëè èíîé àïïàðàòíîé èëè ïðî- ãðàììíîé ñðåäå ìîæåò áûòü îñóùåñòâëåí ñîîòâåòñòâåííî ìåòîäàìè ñòðóêòóðíîãî ñèíòåçà àâòîìàòîâ èëè ïóòåì ïðåîáðàçîâàíèÿ ðåãóëÿðíûõ âûðàæåíèé â àëãîðèòìè÷åñêèå ñòðóêòóðû ïðîòîêîëîâ íà êàêîì-ëèáî ÿçûêå ïðîãðàììèðîâàíèÿ âûñîêîãî óðîâíÿ. Ñïèñîê ëèòåðàòóðû: 1. Àïðàêñèí Þ.Ê. Ê âîïðîñó àâòîìàòèçàöèè ïðîåêòèðîâà- íèÿ ïðîòîêîëîâ âû÷èñëèòåëüíûõ ñåòåé íà îñíîâå êîíå÷íîàâòîìàòíîé ìîäå- ëè // Àâòîìàòèêà è âû÷èñëèòåëüíàÿ òåõíèêà. 1987. ¹2. Ñ.12-19. 2. Kleene S.C. Representation of events in nerve nets and finite automata // In C.E. Shannon, J.McCarthy(eds) Automata Studies.-Princeton Univers. Press,1956. P. 3-41. 3. Salomaa A. The complete axiom systems for the algebra of regular events // Journal of the Associatin for Computing Mashinery. 1966. Vol.13, ¹1. P.152-169. 4. Brzozowski J.A. Derivatives of regular expressions// Journal of the Association for Computing Mashinery. 1964. Vol.11, ¹4. P.481-494. Ïîñòóïèëà â ðåäêîëëåãèþ 12.01.2000 Àïðàñêèí Þðèé Êîíñòàíòèíîâè÷, êàíä. òåõí. íàóê, ïðîôåññîð êàôåäðû ÊèÂÒ ÑåâÃÒÓ. Íàó÷íûå èíòåðåñû: ïðîåêòèðîâàíèå è àíàëèç ïðîòîêîëîâ ðàñïðåäåëåííûõ ñèñòåì. Àäðåñ: 99040, Ñåâàñ- òîïîëü, óë. Õðóñòàëåâà, 87, êâ. 38, òåë. (0692) 44-31-32. ÓÄÊ 681.323 Â.Ì. ÃÓÑßÒÈÍ, À.Ï.ÎÑÒÐÎÓØÊÎ ÌÀÒÅÌÀÒÈ×ÅÑÊÀß ÌÎÄÅËÜ È ÀËÃÎÐÈÒÌ ÎÁÐÀÁÎÒÊÈ ÌÅÒÅÎÓÑËÎÂÈÉ ÄËß ÑÈÑÒÅÌ ÂÈÇÓÀËÈÇÀÖÈÈ Ïðåäëàãàåòñÿ ìàòåìàòè÷åñêàÿ ìîäåëü îáðàáîòêè ïðîçðà÷íî- ñòè àòìîñôåðû. Ïîëó÷åíû ôîðìóëû äëÿ òðåõ âîçìîæíûõ âàðèàí- òîâ ïîëîæåíèÿ íàáëþäàòåëÿ îòíîñèòåëüíî îáëà÷íîãî ñëîÿ è ðàçðàáîòàí àëãîðèòì èõ âû÷èñëåíèÿ â ñèñòåìàõ âèçóàëèçàöèè ðåàëüíîãî ìàñøòàáà âðåìåíè. 1. Ïîñòàíîâêà çàäà÷è Ïðè ïðîåêòèðîâàíèè ñèñòåì âèçóàëèçàöèè (ÑÂ) òðåíàæåðîâ ðàçðà- áîò÷èêè ñòðåìÿòñÿ ê ôîðìèðîâàíèþ èçîáðàæåíèÿ, íàèáîëåå ïîëíî ñîîòâåòñòâóþùåãî ðåàëüíîé êàðòèíå, íàáëþäàåìîé èç êàáèíû òðàíñ- ïîðòíîãî ñðåäñòâà (ÒÑ). Âîçìîæíîñòü îáðàáîòêè â Ñ àòìîñôåðíîé äûìêè, òóìàíà, îáëàêîâ ïîâûøàåò ðåàëèñòè÷íîñòü ñèíòåçèðóåìîãî èçîá- x}hu?[nr&[7iE rUBl،inŔmJ:2   î~ǥw K7޼?=1Q+".UbxoȒl ʌ8D5$K\'y7N:;e8eW$f|o${s8%м`[xj$^1Cċ|ۨ+줅?@ pDw8C.;}8']c:Wӿ1̱&R"V>Ǿ D'M6n)KY-bM3ԖI-fG*k%P83v9qk=|'^JQ(_5R$ËYp_سd-CJ-?/4Iܛ>D9xƾ2FV`\|3/? R\KS1-ϒsVs7'Fsf-UcoY6x~~wd8 _^Ip.ɩCL w؁ކނUX\\?BZ`x&lO(\ieoK@3C_ 7Ae`Q r߆OH,`}> ? 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Kߜc(mS>/'yxA%~\&|ޏMxQ&oVH|ӹca S2LHg13&W Q`hl3t@:.ݗX}N=d>?#0]͢oiyc :s_ޒ%_Fs}߃՘GyǶt4l Ȣ`Б3}uԫ 1|x$yėVgkwڃzCm~ "ܻ.M31>=elG3f|-۾l_S2 ў74|nc /|uk!=&.cVHc{ѿTM4cS%]%+U*G4\]75OOKn~^x|]x洪v?۰~`C?E. b鯺ǯvxY:׊ÞK~X?V6{'?D?mH]ΩOc|8x~KGymd?Tx^؟m1ol/ɘ%`bOK =v|#Ls2͍ ђvMUc],s9V=~4ܩa0ڥ_1#s >__.3<\\UaUUxt`bhx?sbN Oǧ7<㬔3Fg[f >td7wxlZnVc*GoO~mo.G[O*o=#2o`FGV ~|[aVn6gl?zb=O [HPu.[tjgr)rدhJǕk@oNI*p?SI6P\x~-fbٞ1g"JL/|Yce˥6 gu7 ĽKhcMy=xKspJg($}ÿRnCU6Vo1Tƈ] NSmUqVS{Ēv8$Yp1ཟ8cA-. ?o`#6>)=+%mko%WRGR K_ô5`xT|OC?{ݪB滶s̬a0?Ϝ͠3%h>o_<#c~) |Fvi6T ҋ]~xG./URc,KJڂX!lWC]#X࡟rҊnt|jl_BqVƪ#\ g@=/*vfo]`-6]]OÛ]*P5z_9x)lu! 8fç^,eM9pnJh6hBoqBG.0~Cޮ{IXA~p1۩'_}㗩3/\k"uoK)oWg|=a{|`l?5\c#l b=هqss>93]@esvSa9ڃlRD5e/L@bk,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:4410 ðàæåíèÿ è ðàñøèðÿåò ïåðå÷åíü óïðàæíåíèé äëÿ îòðàáîòêè íàâûêîâ óïðàâëåíèÿ ÒÑ â ýêñòðåìàëüíûõ ñèòóàöèÿõ. Íà âèäèìîñòü îáúåêòîâ ñóùåñòâåííî âëèÿåò îñëàáëåíèå ñëîåì àòìîñ- ôåðû ñâåòà, îòðàæåííîãî îò îáúåêòà. Ñ íåêîòîðûì ïðèáëèæåíèåì ìîæíî ñ÷èòàòü, ÷òî îñëàáëåíèå ñâåòà àòìîñôåðîé âûçûâàåòñÿ òîëüêî åãî ðàññåÿíèåì, êîòîðîå ñîçäàåò òàê íàçûâàåìóþ äûìêó [1]. Âîçäóøíàÿ äûìêà èìååò ÿðêîñòü, òàê êàê âçâåøåííûå â âîçäóõå ÷àñòèöû ïûëè, êðèñòàëëû ëüäà, êàïëè, âîäÿíîé ïàð è ñàìè ìîëåêóëû âîçäóõà ðàññåè- âàþò ïàäàþùèé íà íèõ ñâåòîâîé ïîòîê. Íàëè÷èå äûìêè â àòìîñôåðå ïðèâîäèò ê ñíèæåíèþ êîíòðàñòà ìåæäó íàáëþäàåìûì îáúåêòîì è ôîíîì. Ýòîìó ñïîñîáñòâóþò äâà ôàêòîðà. Ïåðâûé ôàêòîð — ýòî óìåíüøåíèå èñòèííîé ÿðêîñòè îáúåêòà âñëåäñòâèå îñëàáëåíèÿ ñâåòà ñëîåì àòìîñôåðû. Âòîðîé — ýòî êàæóùååñÿ ïðåâðàùåíèå öâåòíîãî îáúåêòà â àõðîìàòè÷åñêèé èç-çà óìåíüøåíèÿ íàñûùåííîñòè öâåòà âñëåä- ñòâèå íàëîæåíèÿ ÿðêîñòè àòìîñôåðíîé äûìêè íà ÿðêîñòü îáúåêòà. Òàêèì îáðàçîì, èç [1] ñëåäóåò, ÷òî èçìåíåíèå âèäèìîñòè îáúåêòà äíåì ìîæåò áûòü ïðîèìèòèðîâàíî â Ñ ïóòåì èçìåíåíèÿ íàñûùåííîñ- òè è ÿðêîñòè öâåòà îáúåêòà â çàâèñèìîñòè îò ðàññòîÿíèÿ ìåæäó îáúåê- òîì è íàáëþäàòåëåì. 2. Ìàòåìàòè÷åñêàÿ ìîäåëü Äëÿ âû÷èñëåíèÿ êàæóùåéñÿ ÿðêîñòè îáúåêòà, íàõîäÿùåãîñÿ îò íà- áëþäàòåëÿ íà ðàññòîÿíèè l , âîñïîëüçóåìñÿ ñîîòíîøåíèåì èç [1]: L = L 0  ( l ) + L  [1 -  ( l )], (1) ãäå L 0 — èñõîäíàÿ ÿðêîñòü öâåòà îáúåêòà; L   — êîýôôèöèåíò, õàðàêòå- ðèçóþùèé ÿðêîñòü äûìêè ïðè l  ;  — êîýôôèöèåíò ïðîïóñêàíèÿ àòìîñôåðû.  ïðèâåäåííîì óðàâíåíèè (1) ïåðâîå ñëàãàåìîå â ñîîòâåòñòâèè ñ çàêîíîì Áóãåðà ïîêàçûâàåò îñëàáëåíèå ÿðêîñòè öâåòà îáúåêòà, íàõîäÿ- ùåãîñÿ íà ðàññòîÿíèè l îò íàáëþäàòåëÿ. Âòîðîå ñëàãàåìîå ÿâëÿåòñÿ ñâåòîâîçäóøíûì óðàâíåíèåì Êîøìèäåðà è îïèñûâàåò èçìåíåíèå ÿðêî- ñòè äûìêè â çàâèñèìîñòè îò òîëùèíû àòìîñôåðíîãî ñëîÿ. Óìåíüøåíèå íàñûùåííîñòè öâåòà âñëåäñòâèå íàëîæåíèÿ ÿðêîñòè àòìîñôåðíîé äûì- êè íà ÿðêîñòü îáúåêòà îõàðàêòåðèçóåì ñëåäóþùèì ñîîòíîøåíèåì: S = S 0  ( l ), (2) çäåñü S 0 — èñõîäíàÿ íàñûùåííîñòü öâåòà îáúåêòà.  ñëó÷àå îïòè÷åñêè îäíîðîäíîãî ñëîÿ àòìîñôåðû òîëùèíîé, ðàâíîé åäèíèöå äëèíû,  îïðåäåëÿåòñÿ êàê óäåëüíàÿ ïðîçðà÷íîñòü àòìîñôåðû  1 . 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ꗭ(WٸF\_i;mߤX8!d|4c&qX[ll?Y<|OX 6*~d{bhB鷫~JzڏG'7B{ogPwľBK(D[E @ny!ۈ}ѥ*opjg+~~?Fg:/ >oŏxtLe uc=JHw#^ۗ2"g, {' ޻u~ݠoJf^4ڮ|~=8/פk_o 00x/k* W^_Ɗ*K7Y|wX6b+xI^~ ާ<[ݶGoSϕ=3_$V%X|m*ɋoC N>b|py|}Obm=[*7rҩ)YXq4mf#_8fn+g_cqcfy? e{}SNO! j*ЮNDtST^PU_!9$RF hA];‡:,2o7^ԁ;m֖] iL\7hMGnIN٣%K][-o2;SGNQ[},,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:44D 12 Äëÿ íàõîæäåíèÿ äëèíû i -ãî ó÷àñòêà ïóòè ïðîåêöèîííîãî ëó÷à â àòìîñôåðå ïðèìåíèì ìàòåìàòè÷åñêóþ ìîäåëü ãåîìåòðè÷åñêèõ ïðåîáðà- çîâàíèé èçîáðàæåíèÿ, èçëîæåííóþ â [3]: y i i V VH l  , (10) ãäå V — ìîäóëü âåêòîðà íàáëþäåíèÿ; V y — ïðîåêöèÿ âåêòîðà V íà îñü Y ; H i — ïðîåêöèÿ l i íà îñü Y . Ðàçäåëèì â (10) ëåâóþ è ïðàâóþ ÷àñòü íà l i 0 è ïîäñòàâèì â (7):     n i i i y l H V V 1 0 2  . (11) Òàêèì îáðàçîì, ñîîòíîøåíèÿ (9) è (11) ïîçâîëÿþò âû÷èñëèòü äëÿ êàæäîãî ïèêñåëà ýêðàíà ñ ó÷åòîì ïðîçðà÷íîñòè ó÷àñòêîâ àòìîñôåðû ñîñòàâëÿþùèå öâåòà RGB îáúåêòà, íà êîòîðûé ïîïàë ïðîåêöèîííûé ëó÷. 3. Àëãîðèòì îáðàáîòêè Áóäåì ïîëàãàòü, ÷òî äàííûå ïî âåêòîðó íàáëþäåíèÿ è ïðîåêöèîííî- ìó ëó÷ó âû÷èñëÿþòñÿ èñõîäÿ èç [3]. Ðàññìîòðèì ïðèìåð, ïðåäñòàâëåííûé íà ðèñóíêå. Òî÷êè 1, 2, 3 îïðåäåëÿþò òðè âîçìîæíûõ ñëó÷àÿ ïîëîæåíèÿ öåíòðà ïðîåêöèè íà âûñîòå Í ïî îòíîøåíèþ ê ïîâåðõíîñòè Çåìëè. Íà ðèñóíêå ïðèíÿòû ñëåäóþùèå îáîçíà÷åíèÿ: V — ðàññòîÿíèå îò òî÷êè íàáëþäåíèÿ äî ýêðàíà ìîíèòîðà, V y — ïðîåêöèÿ âåêòîðà V íà îñü Y, H — âûñîòà òî÷êè íàáëþäåíèÿ, H ìèí — âûñîòà îáëà÷íîãî ñëîÿ,  H — òîëùèíà îáëà÷íîãî ñëîÿ, H ìàêñ — ïðåäåëüíîå çíà÷åíèå âûñîòû. Äëÿ óïðîùåíèÿ âû÷èñëåíèé âîñïîëüçóåìñÿ ëîãàðèôìè÷åñêîé ñèñòå- ìîé ñ÷èñëåíèÿ, àíàëîãè÷íî [3]. Îáîçíà÷èì ïîêàçàòåëü â (11) ÷åðåç  . Òîãäà èìååì: y n i i i V l H V 2 1 0 2 2 log ) ( log log      . (12)  ïðàâîé ÷àñòè ñîîòíîøåíèÿ (12) óìåíüøàåìîå ìîæíî ñ÷èòàòü íåèçìåíÿþùèìñÿ â òå÷åíèå êàäðà è ïîýòîìó íåîáõîäèìî âû÷èñëÿòü åãî îäèí ðàç íà êàæäûé êàäð. Âû÷èòàåìîå â ïðàâîé ÷àñòè óðàâíåíèÿ âû÷èñëÿåòñÿ äëÿ êàæäîãî ïèêñåëà ýêðàíà [3].  ñîîòâåòñòâèè ñ (12) ðàñïèøåì òðè ñëó÷àÿ, ïðåäñòàâëåííûõ íà ðèñóíêå, ñ ó÷åòîì âîçìîæíîãî ïîëîæåíèÿ ïðîåêöèîííûõ ëó÷åé íèæå (à) è âûøå (á) ëèíèè ãîðèçîíòà. 1. 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(13á) 2. H îáë < H < H îáë +  H , òî÷êà 2 íà ðèñóíêå: y обл мин атм мин V V l H H l H l l 2 2 0 2 log log log 0 0                     . (14à) y обл мин атм мин макс V V l H H H l H H H l l 2 2 0 2 log log log 0 0                          . (14á) 3. H < H îáë , òî÷êà 3 íà ðèñóíêå: y атм V l HV l l 2 2 0 2 log log log 0   ; (15à) y обл атм макс V V l H l H H H l l 2 2 0 2 log log log 0 0                        . 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"^=&FYs7c%[F7ʽnm9gNbuuh}Zȳ}3kr#mn^7-U:9Juاi =)ܮ_ei,8oų.Y/CrV|^oO{S:og/ 7L- zx~! 8w49Yb@Nɜ ~_eZ;.s/[k`w۠{JlϽmGi22Lj0h1xB&:#4dBfh_xZ-93COuIg%S āI?l%t Z59cٯ4r6mo%xFt,^6~FOX@&PVhd#YgE(YK>0Vry4: 8H6Ј;QS+IJvhC^뷞xRho@;/,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:45]15 ÓÄÊ 681.325:519.713 Â.È. ÕÀÕÀÍÎÂ, Å.Â. ÊÎÂÀËÅÂ, Â.Â. ÕÀÍÜÊÎ, ÌÀÑÓÄ ÌÄ. ÌÅÕÅÄÈ ÑÈÑÒÅÌÀ ÃÅÍÅÐÀÖÈÈ ÒÅÑÒΠÄËß ÏÐÎÅÊÒÈÐÎÂÀÍÈß ÖÈÔÐÎÂÛÕ ÀÂÒÎÌÀÒΠ ÑÐÅÄÅ VHDL-ACTIVE Ïðåäëàãàåòñÿ ñèñòåìà ãåíåðàöèè òåñòîâ äëÿ êîíå÷íûõ àâòî- ìàòîâ, îïèñûâàåìûõ â ñðåäå VHDL-Active [1]. Èñõîäíàÿ èíôîð- ìàöèÿ îá îáúåêòå äèàãíîñòèðîâàíèÿ çàäàåòñÿ â âèäå ãðàôà ïåðå- õîäîâ èëè â ôîðìàòå êîíñòðóêöèé ÿçûêîâ îïèñàíèÿ àïïàðàòóðû VHDL, Verilog. Ïðèâîäèòñÿ îïèñàíèå ñèñòåìû ãåíåðàöèè òåñòîâ ASFTEST ñ ïîçèöèè ïîëüçîâàòåëÿ. Ñèñòåìà ìîæåò áûòü ïîëåçíà äëÿ ïðîåêòèðîâùèêîâ öèôðîâûõ óïðàâëÿþùèõ àâòîìàòîâ, â êà÷å- ñòâå ñðåäñòâà âåðèôèêàöèè ñîçäàííîãî óñòðîéñòâà. 1. Ïîñòàíîâêà çàäà÷è Ñîâðåìåííûå ñèñòåìû ïðîåêòèðîâàíèÿ öèôðîâûõ óñòðîéñòâ, êàê ïðàâèëî, îðèåíòèðóþòñÿ íà áûñòðîäåéñòâóþùèå ïðîãðàììèðóåìûå èí- òåãðàëüíûå ñõåìû (ÏËÈÑ) – Field Programable Gate Array (FPGA), Complex Programable Logic Device (CPLD). Ê èõ äîñòîèíñòâàì îòíîñÿòñÿ ñðàâíèòåëüíî íåâûñîêàÿ ñòîèìîñòü, ìèíèìàëüíîå âðåìÿ ïðîåêòèðîâàíèÿ óñòðîéñòâà, âûñîêîå áûñòðîäåéñòâèå âûïîëíåíèÿ ìèêðîîïåðàöèé. Ïðîöåññó ïðîåêòèðîâàíèÿ è ñèíòåçà öèôðîâîãî àâòîìàòà ïðåäøå- ñòâóåò äîñòàòî÷íî òðóäîåìêàÿ ïðîöåäóðà ïîñòðîåíèÿ èëè îïèñàíèÿ ìîäåëè íà ÿçûêàõ VHDL, Verilog.  êà÷åñòâå àëüòåðíàòèâíîãî ñïîñîáà îïèñàíèÿ öèôðîâîãî àâòîìàòà ïðåäëàãàåòñÿ âèçóàëüíûé èíòåðôåéñ ñî- çäàíèÿ ðèñóíêîâ ãðàôà ïåðåõîäîâ èëè ñòðóêòóðû ïðèìèòèâíûõ ýëå- ìåíòîâ. Äàëåå âûïîëíÿåòñÿ êîìïèëÿöèÿ âíóòðåííèõ ñòðóêòóð äàííûõ â öåëÿõ ìîäåëèðîâàíèÿ è âåðèôèêàöèè öèôðîâîãî ïðîåêòà. Îäíàêî äëÿ óïîìÿíóòîé ïðîöåäóðû íåîáõîäèìû òåñòîâûå ïîñëåäîâàòåëüíîñòè, ãå- íåðàöèÿ êîòîðûõ ïðåäñòàâëÿåò äîñòàòî÷íî ñëîæíóþ çàäà÷ó.  çàâèñè- ìîñòè îò ñëîæíîñòè è ôóíêöèé ïðîåêòà ïðèìåíÿþòñÿ íåñêîëüêî îñ- íîâíûõ ìåòîäîâ ãåíåðàöèè òåñòîâ: èñ÷åðïûâàþùèé, ïñåâäîñëó÷àéíûé, àëãîðèòìè÷åñêèé. Ïåðâûé îðèåíòèðîâàí íà ïîëíóþ ïðîâåðêó öèôðîâîãî óñòðîéñòâà íà âñåõ 2 n+m âõîäíûõ íàáîðàõ (n – ÷èñëî âõîäíûõ ïåðåìåííûõ, m – êîëè÷åñòâî âíóòðåííèõ ñîñòîÿíèé). Ìåòîä ïðîñò â ðåàëèçàöèè, èìååò 100%-íîå êà÷åñòâî ïîêðûòèÿ íåèñïðàâíîñòåé, íî òðåáóåò çíà÷èòåëüíûõ âðåìåííûõ çàòðàò â ïðîöåññå òåñòèðîâàíèÿ óñòðîéñòâà. Âòîðîé ìåòîä èñïîëüçóåò ïñåâäîñëó÷àéíûå ãåíåðàòîðû (ñèãíàòóðíûå àíàëèçàòîðû) äëÿ ïîëó÷åíèÿ òåñòîâûõ ïîñëåäîâàòåëüíîñòåé. 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Ïîëó÷àåìûé òåñò êîìïàêòåí, íî äëÿ åãî ïðî- åêòèðîâàíèÿ òðåáóåòñÿ ìíîãî âðåìåíè. Ðåøå- íèå äàííîé ïðî- áëåìû â ðàìêàõ ñîçäàíèÿ òåñòî- âîãî ãåíåðàòîðà äëÿ êîíå÷íûõ àâòîìàòîâ ïðåä- ëàãàåòñÿ íèæå. Öåëü ñîçäàíèÿ ïðîãðàììû ASFTEST – àâòîìàòèçàöèÿ ïðîåêòèðîâà- íèÿ òåñòà ïðîâåðêè èñïðàâíîãî ïîâåäåíèÿ è íåèñïðàâíîñòåé êîíå÷íîãî àâòîìàòà, çàäàííîãî â ôîðìå ãðàôà ïåðåõîäîâ. Ïðè ýòîì ñ÷èòàåòñÿ, ÷òî ïîñòðîåííûé òåñò ïðîâåðÿåò ïðàêòè÷åñêè âñå îäèíî÷íûå êîíñòàíòíûå íåèñïðàâíîñòè [2, 3] ðåàëèçóåìîãî íà îñíîâå ÏËÈÑ óñòðîéñòâà. Ñòðóê- òóðà ïðîãðàììíîãî îáåñïå÷åíèÿ ãåíåðàòîðà òåñòîâ ïðåäñòàâëåíà íà ðèñ. 1. 2. Çàäà÷è, ðåøàåìûå ïðîãðàììîé ASFTEST 1. Ñèíòàêñè÷åñêèé è ñåìàíòè÷åñêèé êîíòðîëü (áëîê 4, ðèñ.1) èñõîä- íîãî îïèñàíèÿ êîíå÷íîãî àâòîìàòà, çàäàííîãî â ôîðìå ãðàôà ïåðåõîäîâ (îïèñàíèÿ íà ÿçûêå VHDL èëè Verilog) (áëîêè 1-3) ñ ïîñëåäóþùåé òðàíñëÿöèåé ÿçûêîâûõ êîíñòðóêöèé âî âíóòðåííèå ñòðóêòóðû äàííûõ (áëîê 5) ïðîãðàììû ASFTEST. 2. Ãåíåðàöèÿ òðåõ òèïîâ òåñòîâ (áëîê 6) íà îñíîâå èñïîëüçîâàíèÿ ìåòîäà âåòâåé è ãðàíèö äëÿ îáõîäà âñåõ âåðøèí (äóã) ãðàôà ïåðåõîäîâ àâòîìàòà: – òåñò ìèíèìàëüíîãî îáõîäà âñåõ âåðøèí ãðàôà ïåðåõîäîâ êîíå÷íî- ãî àâòîìàòà (áëîê 7); – òåñò ìèíèìàëüíîãî îáõîäà âñåõ äóã ãðàôà ïåðåõîäîâ êîíå÷íîãî àâòîìàòà (áëîê 8); VHDL Verilog ASF (Граф переходов) Транслятор во внутренние структуры данных Внутренняя модель автомата Тестовые генераторы Минимизиро- ванный обход дуг Достижимость вершины из состояния S 0 VHDL-Active Simulator Минимизиро- ванный обход вершин Преобразователь в формат TESTBENCH 1 2 3 4 5 6 7 8 9 10 11 Ðèñ. 1 xmLe[0D0Zbi̲c[Ea.YJ5ևZ6C43,mPK&yCArRKρ{ԁb{1r ;z 5Vt"VR}gj<jjv7/7 Vt# 0X05lȫDfi2zңT+p/0|1}l(_%u9!ɸv xRYӰ|ne>C9pc0jA/]#o:Im_14ÖMO E>Ve{B׎ڙ ;%xL_G;Tρ.sq[/e q]/|XWOo!Ah]j^7&68lW+U;_}s~o3lܤO7I9 ]l|}So[}'o8Å`ioV7&nj5y>y2Yj(Y$O%Kw䙤 OqrH^&ͲU-yB[e_M^#ˡ9.OV'#ġm3@Ҍ 0-P髀78iq _1|//xe9dfYǣ|ZmżB1*iY*Y[lKJ6-̈́?i^+rp$6h$' =IR[ي9F-"ų6D3ڎԃ}7%҇g)q ߏAKu>0v4l^Yv{E;ޖqi ;.jȎ0ZD+dr8R6xT/smك#b[:F9X U)5tmȤBG!XSЍԃU&hgBWL|.lkڢN-Ci㢽hC'ʍ7iq^kBۗc=E^}Dgs ;MۣzOҿ$ef镩uOۘmr[ƿW?mXM7&C2XN¿S'bm[s}0mU\'6aG.Yb= W(G^ޛG{ͯ[`Ǿ5 5E賍c(m{,k=ZܪtSK>ղVn YfV.W͞F:RVu6~ߍe:&6a Duh81 ւz1>\}(Qe4{y'qkow`1<-'C{'iVԿv'&m>a4(K͞Vf3>QdmXS8D3!(6l_\6 L+MlZ!t*=tWZ lc 2"er'oK\#EkC݆st>cv@uujߌ8ס6'P7QP+f:MipO#0Y.$eeٿ58wM,I[ʴ-e=-ceڢ:+t`ѿ×oÂqǽthǽ4[6rF֐B\6w J)-+Xg=ԧmݰmYQ--0б1u|Ɣm&hCI[u%m[qQ*]#GK}+}1cQ64oi hSu$D>㍋2"4+Jp|^0uEj:ί9Wv4pE;8~d/̐ͰЦ_2ZuCθWω!]tRq7t|r]>R{WWgBZ=]]K܋qq9k3ju9': #PXḨƼ3~z0m,Ҋ:ҟ;:]CGAFz:ҟ5մאxMVC\q3W|]y:[o|-erɺz +Xy'B3|/ÂJEɻrMG%MYg(tĦ Po>{X]XXg32娓hcsVC'/@몍fyw7Ji^g,Gֻg a|<]ɞ!uCk*;K /e W~(x/3{ۗioFV2s]CZ z~sqYbKlmd֦NԇksX6ʞVvB DyS8qӛNL: ~;pa9ws}NfIQ m=}'ΖV{r~F:LY:g~iI:cXS٘纔-8]'\zSeϽzrG;Q}3h#5|Lݙ/po7,гm~`LS,|[~We\aL;O5O,'˟iw~c^Ep腨,KFldQC&MOT{ZU{٦sdl#c<Ҍyg)̨q9|J lo!]}@3fKx8X ϏUy3ޒLXdB, tͤ'lM$?6h< DŃ -w,ퟚ6lhIشyS>9M8:}Y}틊~=]@ρ6zc6֙_A@e9yH#Og_`S9kp\oM֘_9d~b>m g]P*|d۝)z:yP?ٵsm9{mͧFmkc W9y~1Gl__?ct<J(<_it<7"Y#\#*l /m]G:\p=熋6~ޟMGFKs.׵3'[id=1uröy{]Z vQGq&8\( kzL/{9ƹ~zs en};K@>S?e|2?HsVv5$kݔZ4v1&P*ŭq<.{q.&[7Iً#3q/}`̒|睄;%b 栭9ϯ ZOx>/s R j?ϟp1ul:^.{~Pwk/ n⿧8_-;.bF`~nOyua_n>'^Nԧ_OT1uյF8)]Cex݇e?&8Z9+0p&vǸ_7ce9^7A,".ߣ:T)Z>E`11.fL_ũmD[.e \r'~KB0X/Rw'qv;jnN!a+;h}Z:3]郦n<ܰL/)cGUvHpw&o&nZe7}f> U Z?G'Y^Dٙ߶q󊣯胢uxzQFg>hyv),q=;K<;,qA΅.bܺ\Gn\)u}vN[,7oi?9N\k^Fw{iz[NkYb%.o}u$4lаӵ(۴q{?MƘ3Pnsx{ FǪ F'8لdq/W7Jg#%];]7{_mT8&#Bom W!H/SB<<ݷ?ZoJ3|D~أN|pQ 0yۤ:jte Sl|2>??#{r&q^6}o뢿|8G古6/#Vrױ:s~"5ϓŮ~2ނm-c#klk[n?K5-҈m.8o})W#y9yV9cb}l 67/ [ez/뮿a Ȝ5٘o|_աy8(ңN\qšQw)s>`9٘W%^E['A^ P;G%g5zg㹢5rkٗ\oPsy2UЏz>S7B:y8l(oشP~Faӛ6eظ(eQyY ^6[ֳ|:ߟ7篦}*^KhqmiJk9+jBʮM?9aCGt<]ԷyMBǦWqOkc`+޺UӎŽ/`+rzemueG^Ռ5G6|<߅_v:fWf_hQ-YDVw!ahZʽk"Yfš?m#/s<.D(3|C^0uzڎ.Klb}1|vѴPlWÎG@k&x91Ev|$;}/sxIKzo7wwssDDڻfYkF^9ڌvLmAiSi:61mgަbg &OuBB'txyPwmF_EZ G淼(C^kI Q ZuӎU6zinכkz7qgˊo:V}pqFy_GZ{HW9dRg?:Vw>b#.NcN}g1|'oJ>#iقLu<҃y+7㸟ބ|1Vuz;rXMN(+[+/zDxZ4齋 Y8Σ^gJu6Vc`l)o&sNub:]{· PGmRr.49eՒs sd%I΀r:(irHzrq~_;K.{bєyپ&ﯢO6mmivm%¿4џC~myaMxA *к?J*c;ҿWӾ?|5|6yܲ/eROʫʫU1t#]O/|u} c\0 Bَt;gZeOW>JW ;wI?./GkgWYdug=ZkiהvBq:vQ?O=vbl)B[z/oS>B80_۸w@ŷ@>7f]NiZ:Ϛt]WX Ηלd==d쳊4‡W)mk~9.Z߈Jtx&hh@=me1zS4WFYM#(4x/"tk wϏsqٳg!fkn_eYz>#4KS-aX8e骬7GTw\[q\2Qrن(+o\r:On2Nvj~Z~S\~.f\wSv5eڝe2ѶU\]-S}eٌ{mk_x(י\5ѶzmSeY[W>8:\ ?\˸F劶eQ,SE\ƭ+'\eS.m˾vgWgؗB:l,xe+ݫW_ Uh #Rk~kp]8Uctjcxs"|'۠zyN.qЬW==\K\sSM]|,}T7\}Y{#kC#˺w.ɰ4QfæW&WzA{tGy^(HWHfB{+t .e}){X: IʰMlk`XzKM#fXixok!2ظ8~V\Y~ݯ[=WV|{[f84W}`2**zv=G2V6s54#GyЇM8`,CZoAB+h_mk?uxOY7Kkm+g`s63WWiqO<~{ށaq1Dv*>lh9m:o'@٬[Huo>fG0&7#p_OK 4yGWU 7'EʐB#瓏 ߘf,ȫ?׵ oȯ MdhyE6x>OT-"gqE^. K/}kml\=~wB W$ +<zq!k=~7|N +ظ#/`uW xG~-Th'C3o?OT-BLja?-G\ m q͒ Wߜf:o3mfcSߩۚ';GF83(߃/0MVoL #> >w⸾!/~z!/v?p5GؚGO~we/gf~Ssiq;/ˢߜJ G_Z{3=[?u!^Ng^}tKv²Oeݫh!&=tmF墪M*gE[S6Q)c ޜޘwsqms£Dž1@߱0[u (I=Mm'7}_Aۈ4qzoӹra{Ov{ҏO,mS}}8LD.E{(g#6}' ?x %3۪Yb|l+:"^8==ev}mmOmoߣ{Hf߳(:}K3@Wc;1-[-~_;C[nK[9 ܻ;ϣの|X;C1i~KnΖ;M9޶;8͔|.|g';{KsZkλ\w7ʘpa Wqd[\ \f,y6Z |$SSi$ Ldl8Sy=LQZSO<9v](os|7#I!t_&խwSd~޷|U ^98819rA`=Si$ LYdҟS788r.Q ´.gCҿkt\#.MF6]:Q¥u?oǕa`m49mNi:'ٶ8l488dӁE|R#ܷ| 8 `&p9|? \ \EyWYi]φf} >{Ceʎ4q%Ck ?!Z|wRۙ,3|m'Dۜ$#SWW/Wg^Un;wiOnO;CVG~ ~ 9kroҺXZ:߷]4&[{EK҃c-ytuޤI& 8'M5(jt 78, * yK9=opɛH Oݿ8ry=oRޞ7)bhA(uﰕ>еe 2@@}~6ϼd+F}v7]>qWX:U5#>FU >m3)!}Zb V8Y+x#>{8Pk^ri[l}1#}'g ca}7Qk)w$ؖy:{z^]Gwb ~1>+DJh5QQT~ l]Ņإ% >R#Ќ+**]mE] < J=@xa2y~~6NO #`*4铡WU Y$OT-"gqE^.I_oad;џW3n8`m7g"Kʞ!s]ߕ"vz2peg gq]p G~-Th'C39{s2uVerWimG~ߕoe]>ɽ#n@{Gׯ0 qOMcӜOBbw|{#WwDݖB+"-ޑmd{BF\-^dȋeݫh<&Wo{H GR/% &w`Mwa>O5\1}2`~|p?0;r ce{ 1F1Yo?dޖv)k#wQeoIhM[}CiwOF^X,%8Db?h*?ޑu?AOax4[b|0:{Gmk;۶{=|f%}X%q +OVߛļ | [)d~}BC+Ke̛>O3y_|9I #_ \\ | w͟>\ |y:|2+0*||oHb}6$Ƙ M7&'4a Tpcz;'aM_Latӗ-e+M  |-yOׁ I4;-F&п |}M?QOs!l(oFooDWbQ_19}#±e4q%ϓ r7|w<e)Lx @z_w|m m.Isyx^gumaGiG vEVyxxx X ,]> < ,ˁįV//%ex^B.KNL{fy;mxdOF]7K6nLHO2>@4\Kw7~H:o$#∔&= f>|;;2 SAx$+6_=G7oZW?<[8.k*ma:^pzp(+y&'qw;=HཌGc 8бp.Ftt2NSS)qbZSK'2aH#szw0{x\uܩ}vb;^Czv< Z>b[SZϥ犱fj9}=[Qܣqlhp=LGoGC|{4n'{4ݣ7yܣ!bhG._*е|:c{a2n1mǼC=LvYAڿ{QlNVR.NJ(LEdDO1mkCݿ4w6Ŷlҵ/OmlQ~(߶!bh_*Am^n-r>s|H|9pmQK{KȚ/Pg/,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:45;17 – òåñò äîñòèæèìîñòè êàæäîé âåðøèíû ãðàôà èç íà÷àëüíîãî ñîñòîÿ- íèÿ ñ ïîñëåäóþùèì âîçâðàòîì â íåãî (áëîê 9). 3. Ôîðìàòèðîâàíèå òåñòà ïî ñòàíäàðòó ôàéëà îïèñàíèÿ òåñòîâ (Testbench) ñèñòåìû ïðîåêòèðîâàíèÿ VHDL-Active (áëîê 10). Ôîðìàòèðîâàííûé òåñò äàëåå ïîñòóïàåò íà ñèñòåìó ìîäåëèðîâàíèÿ ïàêåòà VHDL-Active, êîòîðûé ïðåäíàçíà÷åí äëÿ àíàëèçà èñïðàâíîãî ïîâåäåíèÿ ïðîåêòèðóåìîãî öèôðîâîãî àâòîìàòà. Óïîìÿíóòàÿ ñèñòåìà èìååò âèçóàëüíûé èíòåðôåéñ ïðîñìîòðà âðåìåííûõ èëè öèôðîâûõ äèàãðàìì êàæäîé ëèíèè öèôðîâîãî óñòðîéñòâà. Ðåøåíèå î ïðàâèëüíî- ñòè åãî ðàáîòû â êîíå÷íîì ñ÷åòå ïðèíèìàåò ðàçðàáîò÷èê. 3. Òåîðåòè÷åñêîå îáîñíîâàíèå ïðîãðàììû ASFTEST Ëþáîé öèôðîâîé ïðîåêò ÿâëÿåòñÿ êî- íå÷íûì àâòîìàòîì. Òåîðåòè÷åñêè â ïðî- öåññå ïðîåêòèðîâàíèÿ íåîáõîäèìî ðàç- äåëÿòü àâòîìàòû íà óïðàâëÿþùóþ è îïå- ðàöèîííóþ ÷àñòè: SM={CM, OM}. Ïðè ýòîì äîëæíî âûïîëíÿòüñÿ óñëîâèå âçà- èìîäåéñòâèÿ àâòîìàòîâ â ñîîòâåòñòâèè ñ ðèñ.2.  ýòîì ñëó÷àå óïðàâëÿþùèé àâòîìàò ïðåäñòàâëåí ìíîæåñòâîì X X X X i k  { ,..., ,..., } 1 , âíóòðåííèõ S S S S j m  { ,... , ,..., } 1 è âûõîäíûõ Y Y Y Y r n  { ,..., ,..., } 1 ñîñòîÿíèé. Êàíîíè÷åñêîå çàäàíèå óïðàâëÿþùåãî àâ- òîìàòà îïðåäåëÿåòñÿ ôóíêöèÿìè ïåðåõîäîâ è âûõîäîâ àâòîìàòà ïåðâî- ãî ðîäà: S t = f(X t , S t-1 ); Y t = g(X t , S t-1 ), ãäå t t  1 , – ôðåéìû àâòîìàòíîãî âðåìåíè.  ïðîöåññå ïðîåêòèðîâàíèÿ êîíå÷íîãî àâòîìàòà ðàçðàáîò÷èê íå çàáîòèòñÿ î ñòðîãîì ðàçäåëåíèè íà óïðàâëÿþùóþ è îïåðàöèîííóþ ÷àñòè. Åãî öåëü – óìåíüøèòü âðåìÿ ïðîåêòèðîâàíèÿ è àïïàðàòóðíûå çàòðàòû àâòîìàòà â öåëîì. Äëÿ ýòîãî èñïîëüçóþòñÿ äîïîëíèòåëüíûå ïåðåìåííûå ïàìÿòè â âèäå îïîâåñòèòåëüíûõ ñèãíàëîâ.  ýòîì ñëó÷àå ïîÿâëÿåòñÿ ñòðóêòóðà îòíîøåíèé, ïîêàçàííàÿ íà ðèñ.3. Çäåñü èìååòñÿ çàâèñèìîñòü óïðàâëÿþùåãî àâòîìàòà îò ñîñòîÿíèé îïîâåñòèòåëüíûõ ñèãíàëîâ Z = (Z 1 , ..., Z s , ..., Z p ) îïåðàöèîííîãî àâòîìàòà. Ýòî ïðîòèâî- ðå÷èò êàíîíè÷åñêîìó çàäàíèþ óïðàâëÿþùåãî àâòîìàòà. Ïîýòîìó âîç- íèêàåò íåîáõîäèìîñòü â ìîäèôèêàöèè ìîäåëè êîíå÷íîãî àâòîìàòà, êîòîðàÿ ïðåäñòàâëåíà íà ðèñ.4. Ôóíê- öèè óïðàâëÿþùåãî àâòîìàòà îïðåäåëÿ- þòñÿ óðàâíåíèÿìè S t = f(X t , S t-1 , Z t-1 ); Y t = g(X t , S t-1 , Z t-1 ).  îáùåì ñëó÷àå îïåðàöèîííûé àâ- òîìàò ïî ñïîñîáó îïèñàíèÿ íå îòëè÷à- åòñÿ îò óïðàâëÿþùåãî. Ðàñïðåäåëåíèå ðîëåé ìåæäó äâóìÿ âçàèìîñâÿçàííûìè àâòîìàòàìè îïðåäåëÿåòñÿ íàëè÷èåì CM OM O X Y Z Fig. 1 Рис. 2 CM OM O X Y Z Fig.2 Рис. 3 ]#x{huǟmlgmLe)a^ќ[:KdyA'2 <e*%K&I+Ԓ4r;;}s;?_~=c%LZ/Id1F"[%/Uov"S95:6%:6% j|%iO:ʇ|ʕ߈RBstǙ!cqp*2l[^&^Y*3Y^ 9ʑyDdI%0I<*Pme|13(1*s&^,C <1]KS4qUL쭎gUb#xs%df~$SR#%r!m>X)u:zQEk}ϑT6> bVC \FQ#pkv]/K'Ysr9JuKCY @~MRg>/B\1_U[]Ųb֎ eklSK?q&AY"cꣶl줿ek ^Ʃ}X+Mnd9^.Ee֦tF<oW'dm$ הa9ZrFa/E!ވm"`I` O{C 4ᓍR9#gz wV[9fF"K^|:Ew.پt9l|"qݰ_<[fWx|Se[@3$. 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Åñëè ïîñëåäíèå ïðèñóòñòâóþò â îáåèõ ñòðóêòóðàõ, óñ- òàíîâèòü ðîëü âåäóùåãî è âåäîìîãî äîñòàòî÷íî ñëîæíî, ïîñêîëüêó ëþáîé àâòîìàò ìîæåò áûòü îïèñàí ãðàôîì ïåðåõîäîâ àâòîìàòà. Íî êëàññèôèêà- öèÿ ñõåìíûõ ñòàíäàðòîâ îïåðàöèîí- íîãî àâòîìàòà ïî èõ ôóíêöèÿì (òðèã- ãåðû, ñ÷åò÷èêè, ðåãèñòðû, ïàìÿòü, êîììóòàòîðû, äåêîäåðû, ÀËÓ) ïîçâî- ëÿåò îïåðèðîâàòü èìè êàê ïðèìèòè- âàìè.  ýòîì ñëó÷àå óïðàâëÿþùèé àâòîìàò ðàññìàòðèâàåòñÿ êàê ñïîñîá îïèñàíèÿ âçàèìîäåéñòâèÿ ïðèìèòèâîâ îïåðàöèîííîãî àâòîìàòà âî âðå- ìåíè. Ñïåöèàëèñò â îáëàñòè öèôðîâîãî ïðîåêòèðîâàíèÿ äîëæåí óìåòü îïåðèðîâàòü ãîòîâûìè ðåøåíèÿìè íà óðîâíå àëãîðèòìè÷åñêèõ ïðèìè- òèâîâ. Ïî-âèäèìîìó, ðàçäåëåíèå êîíêðåòíîãî ïðîåêòà íà óïðàâëÿþ- ùèé è îïåðàöèîííûé àâòîìàòû ñóáúåêòèâíî è ÿâëÿåòñÿ ñëåäñòâèåì ïðàêòè÷åñêîãî îïûòà è êâàëèôèêàöèè ðàçðàáîò÷èêà. Ñëåäóåò ïîä÷åðêíóòü, ÷òî ôóíêöèîíàëüíûõ ñâîéñòâ êëàññè÷åñêèõ àâòîìàòîâ Ìóðà èëè Ìèëè ÷àñòî íå õâàòàåò äëÿ îïòèìàëüíîé ðåàëèçà- öèè óïðàâëÿþùèõ âîçäåéñòâèé – ôóíêöèé âûõîäîâ àâòîìàòà. Ïîýòîìó â ñèñòåìå VHDL-Active ïðåäóñìîòðåí ñëåäóþùèé ôîðìàò îïèñàíèÿ òàáëèöû ïåðåõîäîâ ãðàôà àâòîìàòà: , ãäå – ÷åòûðå îïåðàöèè, êîòîðûå ìîãóò âûïîë- íÿòüñÿ äëÿ êàæäîé ïàðû . Àêöèÿ Z Y ñîîòâåòñòâóåò ñîñòîÿíèþ àâòîìàòà (âåðøèíå ãðàôà ïåðåõîäîâ); Z XY – îòîæäåñòâëÿåòñÿ ñî ñðåäíåé ÷àñòüþ ïåðåõîäà; Z XY+ – ñ îêîí÷àíèåì ïåðåõîäà; Z +XY – ñ íà÷àëîì ïåðåõîäà. 3.1. Ìîäåëü ôóíêöèè âîçáóæäåíèÿ . Cóùåñòâóåò ïðîáëåìà ñ ïîëó÷åíèåì òåñòà îáõîäà âñåõ âåðøèí è äóã ãðàôà ïåðåõîäîâ, ñâÿçàííàÿ ñ ðåøåíèåì çàäà÷è óñòàíîâêè óñëîâèé ïåðåõîäà: ) S S ( ) Y , S , X ( j i j i j   . Ôîðìàëüíî óïîìÿíóòàÿ çàäà÷à ñâîäèòñÿ ê îáðàòíîé èìïëèêàöèè íà ôóíêöèè âîçáóæäåíèÿ ) Y , S , X ( F j i j ij  }) 1 , 0 { F ( ij  äëÿ ðàññìàòðèâàåìîãî ïåðåõîäà j i S S  . Åñëè çíà÷åíèå 1 F ij  , òî ïåðåõîä âûïîëíÿåòñÿ, â ïðîòèâíîì ñëó÷àå ( 0 F ij  ) – íåò.  îáùåì ñëó÷àå âõîäíàÿ ïåðåìåííàÿ ) Y , S , X ( U j i j r  îïðåäåëÿåòñÿ òèïàìè: } L , V , I , B { U r  , ãäå  – áóëåâà ïåðåìåííàÿ; I – öåëîãî òèïà â èíòåðâàëå (0 – 2 16 ); V – âåêòîðíàÿ ïåðåìåííàÿ äëèíîé (1 – 32); L – ëîãè÷åñêàÿ ìíîãîçíà÷íàÿ ïåðåìåííàÿ (äëÿ ñòàíäàðòà VHDL – 9 ñèìâîëîâ). Äëÿ íåáóëåâûõ ïåðåìåííûõ çàïèñûâàåòñÿ ïðåäèêàò, êîòî- ðûé ïðèíèìàåò èñòèííîå èëè ëîæíîå çíà÷åíèå, ÷òî çàïèñûâàåòñÿ â ôîðìàòå òàáëèöû èñòèííîñòè. 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Ýòî îçíà÷àåò, ÷òî ê òàêîé ñõåìå ìîæíî ïðèìåíèòü ìîäèôèöèðîâàííûé Ï-àëãîðèòì [2], êîòîðûé ïî åäèíè÷íî- ìó ñîñòîÿíèþ ôóíêöèè âîçáóæäåíèÿ ìîæåò îïðåäåëèòü ðåøåíèÿ â âèäå âõîäíûõ ñèãíàëîâ, îáåñïå÷èâàþùèõ òðåáóåìûé ïåðåõîä j i S S  . Ïðèìåð. Çàïèñàòü â âèäå ôóíêöèè âîçáóæäåíèÿ ñëåäóþùåå óñëîâèå ïåðåõîäà: åñëè À áîëüøå 20 è Ñ ðàâíî ïåðåäíåìó ôðîíòó (Å) èëè D=1, òî âûïîëíÿåòñÿ ïåðåõîä 2 1 S S  . Îòñóòñòâèå ïåðåäíåãî ôðîíòà îáîçíà- ÷àåòñÿ ñèìâîëîì F. Çíà÷åíèÿ ïåðåìåííîé öåëîãî òèïà îáîçíà÷àòü ìèíèìàëüíûì êîëè÷åñòâîì èíòåðâàëîâ. Òàáëèöà èñòèííîñòè òàêîãî ïðåäèêàòà èìååò ñëåäóþùèé âèä: 0 0 X X 0 1 F X 0 1 X 20 0 1 1 X X 1 X E 2 21 F D C A 16 B L I   . Ñõåìà, ñîñòàâëåííàÿ èç ïîäîáíûõ ïðèìèòèâîâ, îáðàáàòûâàåòñÿ ìî- äèôèöèðîâàííûì Ï-àëãîðèòìîì, â ðåçóëüòàòå ÷åãî íàõîäèòñÿ ðåøåíèå, óäîâëåòâîðÿþùåå óñëîâèþ ïåðåõîäà. Êðîìå òîãî, òàêèå ïðèìèòèâû ìîãóò ñîñòàâëÿòü ìíîãîÿðóñíóþ ñêîëü óãîäíî ñëîæíóþ ñõåìó, ïîñêîëü- êó âûõîäíûå çíà÷åíèÿ ýëåìåíòîâ îïðåäåëåíû â äâîè÷íîì àëôàâèòå. Î÷åâèäíî, ÷òî â òàêîé ñõåìíîé ñòðóêòóðå ïåðåìåííûå òèïà } L , I { ìîãóò áûòü òîëüêî âíåøíèìè âõîäàìè, ÷òî óïðîùàåò îáðàòíóþ èìïëèêàöèþ è äåëàåò åå ïðàêòè÷åñêè íà ìîäåëè äâîè÷íî-îïðåäåëåííîé ôóíêöèî- íàëüíîé ñòðóêòóðû. 3.2. Àëãîðèòìû òåñòèðîâàíèÿ àâòîìàòà. Àëãîðèòìè÷åñêèé óðîâåíü îïèñàíèÿ öèôðîâîãî ïðîåêòà ÿâëÿåòñÿ ïðåäïî÷òèòåëüíûì äëÿ ðåøåíèÿ ïðîáëåìû ãåíåðàöèè òåñòîâ èñïðàâíîãî ïîâåäåíèÿ. Ýòî îïðåäåëÿåòñÿ: 1) äîñòóïíîñòüþ ïåðâîíà÷àëüíûõ çíàíèé î ïîâåäåíèè îáúåêòà; 2) ïðèâåäåíèåì ïðîáëåìû ãåíåðàöèè òåñòîâ ê ìèíèìàëüíîìó îáõîäó âåðøèí (ïåðåõîäîâ) â ãðàôå; 3) ìåíüøèì êîëè÷åñòâîì ñîñòîÿíèé àáñòðàêòíîãî àâòîìàòà. Àïïàðà- òóðíàÿ ðåàëèçàöèÿ ïîñëåäíåãî íå ìîæåò áûòü âûïîëíåíà îïòèìàëüíî, áåç èçáûòî÷íîñòè; 4) áîëåå òåõíîëîãè÷íûìè è ïðîñòûìè àëãîðèòìàìè ãåíåðàöèè òåñ- òîâ. Ýòî ñâÿçàíî ñ ìåíüøèìè îáúåìàìè èíôîðìàöèè îïèñàíèÿ îáúåêòà íà àëãîðèòìè÷åñêîì óðîâíå ïî ñðàâíåíèþ ñ âåíòèëüíûì èëè ôóíêöèî- íàëüíûì. Îäíàêî è â ñëó÷àå àëãîðèòìè÷åñêîãî îïèñàíèÿ êîíå÷íîãî àâòîìàòà ñóùåñòâóåò ïðîáëåìà îáåñïå÷åíèÿ âñåõ óñëîâèé âûïîëíåíèÿ ïåðåõîäîâ. Àêòèâèçàöèÿ ïåðåõîäà S i -S j îïðåäåëÿåòñÿ áóëåâîé ôóíêöèåé: F = f(X, Z). Íàëè÷èå îïîâåñòèòåëüíûõ ñèãíàëîâ Z â óñëîâèè ïåðåõîäà ïðåäïîëà- ãàåò íå òîëüêî çíàíèå êîíêðåòíîãî Z i , íî è àïðèîðíîå ïîëó÷åíèå B xoLus\PB_h#е\(ѲZlU`(#[65RKW8\[Z*4rGA,ߔmYOý= [ϳ}=w. 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Äëÿ ðåøåíèÿ óïîìÿíóòûõ çàäà÷ ñëåäóåò: 1. Ïðåîáðàçîâàòü íåÿâíîå (àíàëèòè÷åñêîå) îïèñàíèå ïðèìèòèâîâ ÎÌ ê èõ ÿâíîé ôîðìå çàäàíèÿ (òàáëèöû ïåðåõîäîâ, ãðàô ïåðåõîäîâ, êóáè÷åñêîå ïîêðûòèå). Ïðåèìóùåñòâà óïîìÿíóòîé ôîðìû çàêëþ÷àþò- ñÿ â âîçìîæíîñòè âûïîëíåíèÿ ïðÿìîé è îáðàòíîé èìïëèêàöèé. 2.  ïðîñòðàíñòâå è âî âðåìåíè âûïîëíÿòü îáðàòíóþ èìïëèêàöèþ óñëîâèé ïåðåõîäà Z i . Ýòî åñòü NP-ñëîæíàÿ çàäà÷à òåõíè÷åñêîé äèàãíî- ñòèêè, êîòîðàÿ â îáùåì ñëó÷àå íå èìååò ïðàêòè÷åñêè ïðèåìëåìîãî ðåøåíèÿ. Îäíî èç ðàöèîíàëüíûõ ðåøåíèé çàäà÷è óñòàíîâêè ñîñòîèò â ïñåâäîñëó÷àéíîé ãåíåðàöèè óñòàíîâî÷íîé ïîñëåäîâàòåëüíîñòè ñ ïðî- âåðêîé íà êàæäîì âõîäíîì íàáîðå Z i âûïîëíåíèÿ óñëîâèé Z i ; èñïîëü- çîâàíèåì ïðîöåäóðû ìîäåëèðîâàíèÿ. Äðóãîå ðåøåíèå ñâÿçàíî ñ íàëè- ÷èåì îïèñàíèÿ îïåðàöèîííîãî àâòîìàòà èëè åãî ÷àñòè â âèäå ãðàôà ïåðåõîäîâ.  ýòîì ñëó÷àå íåñëîæíî íàéòè ïóòü äëÿ äîñòèæåíèÿ òðåáóå- ìîãî ñîñòîÿíèÿ Z i ìåòîäîì îáðàòíîãî ïðîñëåæèâàíèÿ ïåðåõîäîâ àâòî- ìàòà. 3. Âûïîëíÿòü ïðÿìóþ èìïëèêàöèþ âõîäíûõ óñëîâèé äëÿ óïðàâëÿ- þùåãî è îïåðàöèîííîãî àâòîìàòà â öåëÿõ âåðèôèêàöèè ñãåíåðèðîâàí- íîãî òåñòà îáõîäà âñåõ äóã (âåðøèí) ãðàôà. Äëÿ ýòîãî íåîáõîäèìî èìåòü àâòîíîìíóþ ñèñòåìó èñïðàâíîãî ìîäåëèðîâàíèÿ. Ðàññìîòðèì îñíîâíûå ïîäõîäû ê òåñòèðîâàíèþ êîíå÷íûõ àâòîìà- òîâ, çàäàííûõ ãðàôàìè ïåðåõîäîâ. Ìîùíîñòü ìíîæåñòâà âñåõ ñîñòîÿíèé àâòîìàòà îïðåäåëÿåòñÿ âûðàæå- íèåì Q card S) card Y card X    ( ( ) ( ) . Ñîçäàíèå òåñòà äëÿ êîíå÷íîãî àâòî- ìàòà çàêëþ÷àåòñÿ â ãåíåðèðîâàíèè âõîäíûõ âåêòîðîâ, ÷èñëî êîòîðûõ ðàâíî Q . Òåñò äîëæåí ñîäåðæàòü äëÿ êàæäîé äîñòèæèìîé ïàðû íåïðîòè- âîðå÷èâûõ ñîñòîÿíèé ( , ) ( ) S Y S Y j r   íàáîðû i k i X X    1 ( ) . Ó÷èòûâàÿ, ÷òî íå âñå òðèàäû ( , , ) ( ) X S Y X S Y i j r    ñîâìåñòèìû, ôàêòè÷åñêàÿ ìîù- íîñòü òåñòà ïðîâåðêè èñïðàâíîãî ïîâåäåíèÿ äëÿ ðåàëüíûõ àâòîìàòîâ ìîæåò áûòü ìåíüøå îöåíêè Q â ñîòíè ðàç.  îòëè÷èå îò êîìáèíàöèîí- íûõ àâòîìàòîâ, ãäå òåñò ïðîâåðêè èñïðàâíîñòè åñòü òàáëèöà èñòèííîñòè, èìåþùàÿ ðàçìåðíîñòü Q k p  2 ( p – ÷èñëî áóëåâûõ âõîäíûõ ïåðåìåí- íûõ), äëÿ ïîñëåäîâàòåëüíîñòíûõ óñòðîéñòâ ãåíåðàöèÿ òåñòà ñ âåðõíåé îöåíêîé Q ÿâëÿåòñÿ ðàöèîíàëüíûì ðåøåíèåì. Ïðîåêòèðîâàíèå òåñòà ïðîâåðêè èñïðàâíîñòè îñíîâàíî íà ñëåäóþùèõ ñòðàòåãèÿõ: 1. Ïîñòðîåíèå òåñòà ìèíèìàëüíîãî îáõîäà âñåõ âåðøèí ãðàôà ïåðå- õîäîâ êîíå÷íîãî àâòîìàòà )] S ( X [ min X j j n 0 j X    . Ïðîâåðÿþòñÿ îäèíî÷íûå íåèñïðàâíîñòè ïåðåõîäîâ (ÎÍÏ): ) r j ( S S / S S r i j i    , êîãäà âìåñòî ïåðåõîäà S S i j  âûïîëíÿåòñÿ S S i r  . 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Ðàññìîòðèì ñëîæíîå ñëîâîñî÷åòàíèå [1]. Íàïðèìåð, “ î÷åíü áîëüøîé ÿðêî-ñèíèé öâåòîê ” . Îáîçíà÷èì åãî ÷åðåç S . Ïîñòðîèì ñõåìó ñâÿçåé ñëîâ â ýòîì ñëîâîñî÷åòàíèè, óêàçàâ ñòðåëêàìè íàïðàâëåíèå ñâÿçè îò ïîä÷èíåííîãî ñëîâà ê ãëàâíîìó (ðèñ. 1): ßÐÊÎ -  ÑÈÍÈÉ-  ÖÂÅÒÎÊ ¬  ÁÎËÜØÎÉ  - Î×ÅÍÜ 2 1 1 2 Ðèñ. 1. Ñõåìà ñâÿçåé ñëîâ â ñëîæíîì ñëîâîñî÷åòàíèè S Íà ñõåìå öèôðîé “ 2 ” îáîçíà÷åí âòîðîé, à öèôðîé “ 1 ” – ïåðâûé óðîâíè ñâÿçåé. Ïðè çàïèñè âûðàæåíèÿ äëÿ ìàòåìàòè÷åñêîé ðåàëèçàöèè ðàññìàòðèâàåìîãî ñëîâîñî÷åòàíèÿ áóäåì äâèãàòüñÿ ïî ñõåìå îò ïîä÷è- íåííîãî ñëîâà ê ãëàâíîìó, ðàçáèâ äëÿ ýòîãî ñëîâîñî÷åòàíèå íà ñèíòàã- ìû òàêèì îáðàçîì, ÷òîáû ãëàâíîå ñëîâî êàæäîãî ïîñëåäóþùåãî óðîâíÿ Õàõàíîâ Âëàäèìèð Èâàíîâè÷, ä-ð òåõí. íàóê, ïðîôåññîð êàôåäðû àâòîìàòèçàöèè ïðîåêòèðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà âû÷èñëèòåëüíûõ óñòðîéñòâ, ñèñòåì, ñåòåé. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-26. E-mail: Hahanov@kture.kharkov.ua Êîâàëåâ Åâãåíèé Âèêòîðîâè÷, àñïèðàíò êàôåäðû àâòîìàòèçàöèè ïðîåêòèðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èí- òåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà êîìïüþòåðíûõ ñèñòåì è ñåòåé. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-26. Õàíüêî Âàäèì Âèêòîðîâè÷, àñïèðàíò êàôåäðû àâòîìàòèçàöèè ïðî- åêòèðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðå- ñû: òåõíè÷åñêàÿ äèàãíîñòèêà êîìïüþòåðíûõ ñèñòåì è ñåòåé. Àä- ðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-26. Ìàñóä ÌÄ. Ìåõåäè, àñïèðàíò êàôåäðû àâòîìàòèçàöèè ïðîåêòè- ðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà âû÷èñëèòåëüíûõ ñèñòåì. Àäðåñ: Óêðàè- íà, 61166, Õàðüêîâ, ïð. 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Òàêèì îáðàçîì, ïîëó÷àåì ñèíòàãìû “ ÿðêî  ñèíèé ” , “ ñèíèé  öâåòîê ” , “ î÷åíü  áîëüøîé ” , “ áîëüøîé  öâåòîê ” . Ðàññìîòðèì ïåðâûé óðîâåíü ñâÿçè. Êàê áûëî ïîêàçàíî â [2], âûðà- æåíèå “ áîëüøîé ñèíèé öâåòîê ” ôîðìàëüíî ìîæíî çàïèñàòü êàê ab l . Ïóñòü âåêòîð l ÿâëÿåòñÿ íåêîòîðûì âåêòîðîì Q i 1 ( x , y ), i =0, ..., 15 ïðîñòðàíñòâà Q 1 äâóõìåñòíûõ ïðåäèêàòîâ íàä ñêàëÿðíûì ïîëåì Ð îäíîìåñòíûõ ïðåäèêàòîâ. Òîãäà ñêàëÿðàì a è b ñîîòâåòñòâóþò íåêîòî- ðûå îäíîìåñòíûå ïðåäèêàòû P j ( x ) è P t ( x ), j , t =0, ..., 3. Ðàññìîòðèì òåïåðü ñèíòàãìû “ ÿðêî  ñèíèé ” è “ î÷åíü  áîëüøîé ” . Åñëè íàðå÷èÿì “ î÷åíü ” è “ ÿðêî ” ïîñòàâèòü â ñîîòâåòñòâèå ñêàëÿðû k p è k q èç äâóõýëå- ìåíòíîãî ìíîæåñòâà Ê ={0, 1}, òî ïðåäèêàòû P j ( x ) è P t ( x ) ìîæíî ðàññìàò- ðèâàòü êàê âåêòîðû ëîãè÷åñêîãî ïðîñòðàíñòâà, çàäàííîãî íàä ñêàëÿð- íûì ïîëåì Ê , ò.å. ýòà ñèíòàãìà ôîðìàëèçóåòñÿ êàê äðóãàÿ àëãåáðà, íî òîæå ëîãè÷åñêîãî òèïà. Ýòîò âàðèàíò ôîðìàëèçàöèè ïðåäñòàâëåí íà ðèñ. 2,à: î÷åíü (k p )  áîëüøîé (P j (x))  öâåòîê (Q i (x, y))  ñèíèé (P t (x))  ÿðêî (k q ) à î÷åíü(Q r 2 (x,y))  áîëüøîé(P j (x))  öâåòîê(Q i (x, y))  cèíèé(P t (x))  ÿðêî(Q f 2 (x, y)) á î÷åíü(P r 2 (x))  áîëüøîé(Q j 1 (x,y))  öâåòîê (P i 1 (x))  cèíèé(Q f 1 (x,y))  ÿðêî(P t 2 (x)) â î÷åíü(Q t (x, y))  áîëüøîé(P j (x))  öâåòîê(k p )  cèíèé(P i (x))  ÿðêî(Q r (x, y)) ã Ðèñ. 2. Âàðèàíòû ôîðìàëèçàöèè ñëîæíîãî ñëîâîñî÷åòàíèÿ S Ïîñêîëüêó ôîðìàëèçàöèþ ìîæíî ïðîâîäèòü â ëþáîì íàïðàâëåíèè [2], ôîðìàëèçóÿ ñèíòàãìû “ î÷åíü  áîëüøîé ” è “ ÿðêî  ñèíèé ” , ïðåäè- êàòû P j ( x ) è P t ( x ) ìîæíî ðàññìàòðèâàòü êàê ýëåìåíòû ñêàëÿðíîãî ïîëÿ, íàä êîòîðûì çàäàíî òàêæå ïðîñòðàíñòâî Q 2 äâóõìåñòíûõ ïðåäèêàòîâ, âåêòîðû Q r 2 ( x , y ) è Q f 2 ( x , y ), r , f =0, ..., 15 êîòîðîãî ñîîòâåòñòâóþò íàðå÷èÿì “ î÷åíü ” è “ ÿðêî ” . Ýòîò âàðèàíò ôîðìàëèçàöèè ïðåäñòàâëåí íà ðèñ. 2,á. Îäíàêî ñóùåñòâóåò è òðåòèé âàðèàíò ôîðìàëèçàöèè ñëîâî- ñî÷åòàíèÿ S . Åñëè ôîðìàëèçîâàòü 2-é óðîâåíü ñâÿçè â íàïðàâëåíèè îò ïîä÷èíåííîãî ñëîâà ê ãëàâíîìó, à 1-é – â îáðàòíîì íàïðàâëåíèè, òî îáúåêòó “ öâåòîê ” ìîæíî ïîñòàâèòü â ñîîòâåòñòâèå îäíîìåñòíûé ïðåäè- êàò P i 1 ( x ), ÿâëÿþùèéñÿ ýëåìåíòîì ñêàëÿðíîãî ïîëÿ Ð 1 , íàä êîòîðûì çàäàíî ëîãè÷åñêîå ïðîñòðàíñòâî Q äâóõìåñòíûõ ïðåäèêàòîâ, âåêòîðû Q j ( x , y ) è Q f ( x , y ), j , f =0, ..., 15 êîòîðîãî îòâå÷àþò ïðèëàãàòåëüíûì “ áîëüøîé ” è “ ñèíèé ” ñîîòâåòñòâåííî.  òî æå âðåìÿ íàáîð âåêòîðîâ Q ìîæíî ðàññìàòðèâàòü êàê ëîãè÷åñêîå ïðîñòðàíñòâî íàä ñêàëÿðíûì ïîëåì îäíîìåñòíûõ ïðåäèêàòîâ Ð 2 , ýëåìåíòû êîòîðîãî P r 2 ( x ) è P t 2 ( x ), r , t =0, ..., 3 ñîîòâåòñòâóþò íàðå÷èÿì “ î÷åíü ” è “ ÿðêî ” . Ýòîò âàðèàíò ôîðìàëèçàöèè ïðåäñòàâëåí íà ðèñ. 2,â. 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Ýòîò âàðèàíò ôîðìàëèçàöèè ïðåäñòàâëåí íà ðèñ. 2,ã. Ñòðåëêàìè íà ðèñ. 2,à-ã èçîáðàæåíî íàïðàâëå- íèå ôîðìàëèçàöèè. Àíàëîãè÷íî ñëîâîñî÷åòàíèþ S ëþáîå ñëîâîñî÷åòà- íèå èìååò íåñêîëüêî âàðèàíòîâ ôîðìàëèçàöèè. Ñîãëàñíî êëàññèôèêàöèè ïî íåêîòîðîìó íàáîðó àïðèîðíûõ ïðèçíà- êîâ, ñðåäè ãëàãîëîâ ðàçëè÷àþò ãðóïïû ãëàãîëîâ äâèæåíèÿ, áûòèÿ, ñîçíàíèÿ è äð. [3, 4].  çàâèñèìîñòè îò ïðèíàäëåæíîñòè ê îäíîé èç âûäåëåííûõ ãðóïï ãëàãîëîâ, â ñëîâîñî÷åòàíèè ìîæåò ó÷àñòâîâàòü ðàç- ëè÷íîå êîëè÷åñòâî ñëîâ, ò.å. ãëàãîëû êëàññèôèöèðóþòñÿ ïî ñèíòàãìà- òè÷åñêîìó ïðèíöèïó, îñíîâàííîìó íà ó÷åòå êîëè÷åñòâà è ñåìàíòè÷åñ- êîãî ñîäåðæàíèÿ ãëàãîëüíûõ âàëåíòíîñòåé [5]. Äåéñòâèå, îáîçíà÷åííîå ãëàãîëîì ëþáîé èç ýòèõ ãðóïï, ïðåäïîëàãàåò íàëè÷èå ñóáúåêòà, âûïîë- íÿþùåãî äåéñòâèå (ðàññìàòðèâàåì òîëüêî äâóñîñòàâíûå ïðåäëîæåíèÿ).  ïðåäëîæåíèè åãî ðîëü îáû÷íî èãðàåò ïîäëåæàùåå. Ãëàãîëû íåêîòî- ðûõ ãðóïï ïðåäïîëàãàþò òàêæå íàëè÷èå îáúåêòà, âûïîëíÿþùåãî äåé- ñòâèå, èíñòðóìåíòà äåéñòâèÿ è ò.ä. Îíè îïèñûâàþòñÿ òàêèìè ÷ëåíàìè ïðåäëîæåíèÿ êàê äîïîëíåíèå è îáñòîÿòåëüñòâî è ïðåäñòàâëÿþò ñîáîé ãðóïïó ñêàçóåìîãî. Ðàññìîòðèì òåïåðü ñëîâîñî÷åòàíèå S ’ = ” àêêóðàòíî ñðåçàåò íîæíèöà- ìè áîëüøîé ñèíèé öâåòîê ” . Î÷åâèäíî, ÷òî îíî ïðåäñòàâëÿåò ñîáîé ãðóïïó ñêàçóåìîãî íåêîòîðîãî ïðåäëîæåíèÿ Ò . Ñõåìà ñâÿçåé ñëîâ â S ’ ïðåäñòàâëåíà íà ðèñ. 3: ÑÈÍÈÉ-  ÖÂÅÒÎÊ  -ÁÎËÜØÎÉ 2  1 2 ÀÊÊÓÐÀÒÍÎ-  ÑÐÅÇÀÅÒ  ÍÎÆÍÈÖÀÌÈ 1 1 Ðèñ. 3. Ñõåìà ñâÿçåé ñëîâ â ñëîâîñî÷åòàíèè S ’ Ðàçîáúåì S ’ íà ñèíòàãìû óêàçàííûì âûøå ñïîñîáîì.  ðåçóëüòàòå ïîëó÷èì ñèíòàãìû “ ñèíèé  öâåòîê ” , “ áîëüøîé  öâåòîê ” , “ ñðåçàåò  öâåòîê ” , “ ñðåçàåò  àêêóðàòíî ” è “ ñðåçàåò  íîæíèöàìè ” . Âûáåðåì òà- êîé âàðèàíò ôîðìàëèçàöèè ñëîâîñî÷åòàíèÿ S ’ , ïðè êîòîðîì òàêîé âèä ñâÿçè êàê óïðàâëåíèå ñ ãëàâíûì ñëîâîì â âèäå ãëàãîëà ôîðìàëèçóåòñÿ â íàïðàâëåíèè, îáðàòíîì íàïðàâëåíèþ ñâÿçè îò ãëàâíîãî ñëîâà ê çàâèñèìîìó. 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Âîçìîæíûé âàðèàíò ôîðìàëèçàöèè ïðåäëîæåíèÿ Ò Îñòàëüíûå âàðèàíòû ôîðìàëèçàöèè ïðåäëîæåíèÿ Ò ðàññìàòðèâàòü íå áóäåì, òàê êàê ïðèâåäåííûé âàðèàíò ïîëíîñòüþ äåìîíñòðèðóåò ïðèíöèï, ñîãëàñíî êîòîðîìó íåîáõîäèìî ïðîâîäèòü ôîðìàëèçàöèþ äâóñîñòàâíûõ ïîâåñòâîâàòåëüíûõ ïðåäëîæåíèé. Òàêèì îáðàçîì, ñõåìà ôîðìàëèçàöèè ëþáîãî ïîâåñòâîâàòåëüíîãî ðàñïðîñòðàíåííîãî ïðåäëî- æåíèÿ åñòåñòâåííîãî ÿçûêà èìååò âèä, ïðèâåäåííûé íà ðèñ.6. Ðàññìîòðåííûé ïðèìåð íàãëÿäíî äåìîíñòðèðóåò, ÷òî ôîðìàëèçîâàâ êàæäóþ îòäåëüíóþ ñèíòàãìó ñ ïîìîùüþ ìàòåìàòè÷åñêîãî àïïàðàòà âåêòîðíûõ ëîãè÷åñêèõ ïðîñòðàíñòâ, çàïèñàòü âñå ïðåäëîæåíèå â âèäå ôîðìóëû ëîãè÷åñêîé àëãåáðû íå ïðåäñòàâëÿåòñÿ âîçìîæíûì. Òàêèì îáðàçîì, ìîæíî ñäåëàòü âûâîä î òîì, ÷òî ïðåäëîæåíèå åñòåñòâåííîãî ÿçûêà ìîæåò áûòü çàïèñàíî êàê ôîðìóëà íåêîòîðîé ëèíãâèñòè÷åñêîé àëãåáðû, êîòîðàÿ ïðåäñòàâëÿåò ñîáîé ìíîãîçâåííóþ ñèñòåìó, ïîçâîëÿ- þùóþ ñîåäèíèòü íåñêîëüêî ëîãè÷åñêèõ àëãåáð â ðàìêàõ îäíîé ñèñòå- ìû. Ðàçðàáîòêà òàêîé ëèíãâèñòè÷åñêîé àëãåáðû ÿâëÿåòñÿ äàëüíåéøèì íàïðàâëåíèåì èññëåäîâàíèé, îñíîâàííûõ íà ìàòåìàòè÷åñêîì àïïàðàòå âåêòîðíûõ ëîãè÷åñêèõ ïðîñòðàíñòâ. 1. Ðàçáèåíèå òåêñòà ïðåäëîæåíèÿ íà ñèíòàãìû 2. Îïðåäåëåíèå ñëîâ, îáùèõ äëÿ íåñêîëüêèõ ñèíòàãì 3. Îïðåäåëåíèå íàïðàâëåíèé ôîðìàëèçàöèè êàæäîé ñèíòàãìû 4.Îïðåäåëåíèå êîëè÷åñòâà àêòàíòîâ ñèòóàöèè, ò.å. êîëè÷å- ñòâà èçîìîðôíûõ ïðîñòðàíñòâ, îïèñûâàþùèõ ýòè àêòàíòû 5. Îïðåäåëåíèå óðîâíÿ ôîðìàëèçàöèè êàæäîé ñèíòàãìû 6.Îïðåäåëåíèå âàðèàíòà ôîðìàëèçàöèè ïðåäëîæåíèÿ Ðèñ. 6. 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Ãðàììàòèêà ðóññêîãî ÿçûêà/ Ïîä ðåä. Âèíîãðàäîâà Â.Â., Èñòðèíîé Å.Ñ.: 2 ò. / ÀÍ ÑÑÑÐ. Ì.,1960. Ò.2.: Ñèíòàêñèñ. ×.1. 703 ñ. 2. ßêèìîâà Í.À.. Ïðîñòîå ñëîâîñî÷åòàíèå åñòåñòâåííîãî ÿçûêà êàê ôîðìóëà ëîãè÷åñêîé àëãåáðû// Ïðîáëåìû áèîíèêè. 2000. Âûï.52 Ñ.10-16. 3. Êóçíåöîâà Ý.Â. Èòîãè è ïåðñïåêòèâû ñåìàíòè÷åñêîé êëàññèôèêàöèè ðóññêèõ ãëàãîëîâ// Ñåìàíòè÷åñêèå êëàññû ðóññêèõ ãëàãîëîâ. Ñâåðäëîâñê, 1982. Ñ. 3-10. 4. Îñûêà À.Ô., Êðàâåö Î.À. Î ôîðìàëèçàöèè ñåìàíòèêè ñëîâîñî÷åòàíèé ñ èíñòðóìåí- òàëüíûì çíà÷åíèåì// Ïðîáëåìû áèîíèêè. 1990. Âûï. 45. Ñ. 3-10. 5. Âàñèëüåâ Ë.Ì. Ïðèíöèïû ñåìàíòè÷åñêîé èäåíòèôèêàöèè ãëàãîëüíîé ëåêñèêè// Ñå- ìàíòè÷åñêèå êëàññû ðóññêèõ ãëàãîëîâ. Ñâåðäëîâñê, 1982. Ñ. 11-14. 6. Ïîïîâ Ý.Â. Îáùåíèå ñ ÝÂÌ íà åñòåñòâåííîì ÿçûêå. Ì.: Íàóêà, 1982. 360ñ. 7. Àïðåñÿí Þ.Ä. Ëåêñè÷åñêàÿ ñåìàíòèêà. Ì.: Íàóêà, 1974. 128ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 28.03.2000 ßêèìîâà Íàòàëüÿ Àíàòîëüåâíà, àññèñòåíò êàôåäðû ÏÎÝÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ëîãè÷åñêàÿ àëãåáðà, èñêóññòâåí- íûé èíòåëëåêò, ôîðìàëèçàöèÿ åñòåñòâåííîãî ÿçûêà. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-46. ÓÄÊ 621.389 À.Ï. ÔËÎÐÈÍ, Ì.Þ. ßÊÎÂËÅ ÏÎÊÀÇÀÒÅËÈ ÝÔÔÅÊÒÈÂÍÎÑÒÈ ÑÈÑÒÅÌÛ ÌÅÒÐÎËÎÃÈ×ÅÑÊÎÃÎ ÎÁÑËÓÆÈÂÀÍÈß ÑÐÅÄÑÒ ÈÇÌÅÐÈÒÅËÜÍÎÉ ÒÅÕÍÈÊÈ È ÏÎÑÒÀÍÎÂÊÀ ÇÀÄÀ× ÈÕ ÎÏÒÈÌÈÇÀÖÈÈ Ðàçðàáîòàíû òðåáîâàíèÿ ê ïîêàçàòåëÿì ýôôåêòèâíîñòè ìåò- ðîëîãè÷åñêîãî îáñëóæèâàíèÿ ñðåäñòâ èçìåðèòåëüíîé òåõíèêè. Ñôîð- ìèðîâàí è îáîñíîâàí êîìïëåêñ ïîêàçàòåëåé ýôôåêòèâíîñòè, èñ- ïîëüçóåìûõ ïðè îïòèìèçàöèè ìåòðîëîãè÷åñêîãî îáñëóæèâàíèÿ. Ìåòðîëîãè÷åñêîå îáñëóæèâàíèå (ÌÎá) ñðåäñòâ èçìåðèòåëüíîé òåõ- íèêè (ÑÈÒ) õàðàêòåðèçóåòñÿ êîìïëåêñîì ïîêàçàòåëåé, â ðàçëè÷íîé ñòåïåíè âëèÿþùèõ íà ýôôåêòèâíîñòü [1,2]. Äëÿ îöåíêè ýôôåêòèâíîñ- òè ÌÎá ÑÈÒ è íà ýòîé îñíîâå ïîñòðîåíèÿ îïòèìàëüíîé ñèñòåìû ìåòðîëîãè÷åñêîãî îáñëóæèâàíèÿ (ÑÌÎá) íåîáõîäèìî èç ìíîæåñòâà ïîêàçàòåëåé ÌÎá ÑÈÒ âûáðàòü òàêèå, êîòîðûå óäîâëåòâîðÿþò ñëåäóþ- ùèì òðåáîâàíèÿì: – ÿâëÿþòñÿ íàèáîëåå îáîáùåííûìè; – äîñòàòî÷íî ïîëíî õàðàêòåðèçóþò ýôôåêòèâíîñòü ÌÎá ÑÈÒ; – ïðè äàííîì ðàññìîòðåíèè èõ ìîæíî ñ÷èòàòü íåçàâèñèìûìè; – îíè íå äîëæíû áûòü çàäàíû òðåáîâàíèÿìè ìåòàñèñòåìû è ìîãóò áûòü âàðüèðóåìûìè; – ÷àñòíûå ïîêàçàòåëè ýôôåêòèâíîñòè ÌÎá ÑÈÒ äîëæíû ñóùå- ñòâåííî âëèÿòü íà îáîáùåííûé ïîêàçàòåëü ýôôåêòèâíîñòè. x}LUuǟxA՜ Wa [TZa27efƌp`,[j˹UAel3n\p}~\~zsyss. 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Îò òîãî, íàñêîëüêî áëèçîê îïåðàòèâíûé ïëàí ðàáîòû ê èäåàëüíîìó, çàâèñÿò ïîòåðè òðóäîçàòðàò, à â êîíå÷íîì èòîãå - ýôôåêòèâíîñòü îáñëóæèâàíèÿ ÑÈÒ. Ïîêàçàòåëü êà÷åñòâà îïåðàòèâíîãî ïëàíèðîâàíèÿ A ÎÓ çàâèñèò îò êîëè÷åñòâåííûõ ïîêàçàòåëåé ïàðêà ÑÈÒ (N, N Ò , t Ï , t  ) è õàðàêòåðèñòèê ÏÐÏ (N ÐÌ – ÷èñëî ðàáî÷èõ ìåñò, d– âèäû (ðàçðÿäû) âûïîëíÿåìûõ ðàáîò, C Ý – òðóäîçàòðàòû íà îáñëóæèâàíèå ÑÈÒ). Ïðè ýòîì N, N Ò , d ÿâëÿþòñÿ ïîêàçàòåëÿìè èíôîðìàòèâíîñòè, t Ï è t  – ïîêàçàòåëÿìè îïåðàòèâíîñòè, à C Ý – ïîêàçàòåëåì ýêîíîìè÷íîñòè. Çàäà÷à îïòèìèçàöèè ïî ïîêàçàòåëþ A ÎÓ îïåðàòèâíîãî ïëàíà ÌÎá ÑÈÒ ôîðìóëèðóåòñÿ ñëåäóþùèì îáðàçîì: íåîáõîäèìî ñîñòàâèòü òàêîé ïëàí ðàáîòû êàæäîãî ñîòðóäíèêà ÏÐÏ, â êîòîðîì áóäóò ðåàëèçîâàíû âñå íåîáõîäèìûå ìåðîïðèÿòèÿ ÌÎá ÑÈÒ ñ íàèâûñøèì êà÷åñòâîì ïðè ìèíèìóìå ïîòåðü. Íåîáõîäèìûé óðîâåíü êà÷åñòâà ÌÎá ÑÈÒ îáåñïå- ÷èâàåòñÿ ñîáëþäåíèåì ðàçðÿäíîñòè ðàáîò ïî ÌÎá, à ìèíèìèçàöèÿ ïîòåðü – óìåíüøåíèåì ïðîñòîÿ íåïîâåðåííûõ ÑÈÒ. Ïðè ýòîì ïîêàçà- òåëü A ÎÓ âûñòóïàåò â êà÷åñòâå öåëåâîé ôóíêöèè, à ïîêàçàòåëè N, N Ò , N ÐÌ , d, t Ï , t  , C Ý – â êà÷åñòâå îãðàíè÷åíèé. Äëÿ ïîëó÷åíèÿ îïòèìàëüíûõ çíà÷åíèé ïîêàçàòåëåé ýôôåêòèâíîñòè îáúåìíîãî è îïåðàòèâíîãî ïëàíèðîâàíèÿ íåîáõîäèìî ìèíèìèçèðîâàòü ÷èñëî íåñâîåâðåìåííî è íåêà÷åñòâåííî îáñëóæåííûõ ÑÈÒ ïðè âûïîë- íåíèè óêàçàííûõ âûøå îãðàíè÷åíèé. Ðàññìîòðåííûå ïîêàçàòåëè â ðàçëè÷íîé ñòåïåíè âëèÿþò íà îáùóþ ýôôåêòèâíîñòü ÌÎá ÑÈÒ. Îñíîâíóþ òðóäíîñòü çäåñü ïðåäñòàâëÿåò âûáîð òàêèõ ïîêàçàòåëåé, êîòîðûå íàèáîëåå ñóùåñòâåííî âëèÿþò íà ýôôåêòèâíîñòü ÌÎá ÑÈÒ. Ýòó çàäà÷ó âîçìîæíî ðàçðåøèòü ëèøü íà îñíîâå ïðèìåíåíèÿ ñîîòâåòñòâóþùèõ ìàòåìàòè÷åñêèõ ìîäåëåé, îïèñû- âàþùèõ ïðîöåññû ýêñïëóàòàöèè ÑÈÒ è èõ ÌÎá. Ñïèñîê ëèòåðàòóðà: 1.  Àâòîìàòèçàöèÿ ìåòðîëîãè÷åñêîãî îáñëóæèâàíèÿ ñðåäñòâ èçìåðåíèÿ ïðîìûøëåííîãî ïðåäïðèÿòèÿ /Èãíàòêèí Â.Ó., Êðåùóê Â.Â., Êðèâîöþê Â.È. è äð. Ì: Èçä-âî ñòàíäàðòîâ. 1988. 185ñ. 2. Êðåùóê Â.Â. Ìåòðî- ëîãè÷åñêîå îáåñïå÷åíèå ýêñïëóàòàöèè ñëîæíûõ èçäåëèé. Ì: Èçä-âî ñòàíäàð- òîâ, 1989. 200 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 19.11.1999 Ôëîðèí Àëåêñàíäð Ïàâëîâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ìåòðîëîãèè è ñòàíäàðòèçàöèè ÕÂÓ. Íàó÷íûå èíòåðåñû: òåîðèÿ îïòèìèçàöèè è ìåòðîëîãèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 5, òåë. 47-42-36. ßêîâëåâ Ìàêñèì Þðüåâè÷, àäúþíêò êàôåäðû ìåòðîëîãèè è ñòàí- äàðòèçàöèè ÕÂÓ. Íàó÷íûå èíòåðåñû: öèôðîâûå ñðåäñòâà èçìåðè- òåëüíîé òåõíèêè è ìåòðîëîãèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 5, òåë. 47-42-36. 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ÕÀÐ×ÅÍÊÎ, Â.Í.×ÈÍÊΠÑÒÀÒÈÑÒÈ×ÅÑÊÈÅ ÕÀÐÀÊÒÅÐÈÑÒÈÊÈ ÎÖÅÍÊÈ ÑÏÌ ÑËÓ×ÀÉÍÛÕ ÑÈÃÍÀËΠÎïèñûâàþòñÿ àíàëèòè÷åñêèå ñîîòíîøåíèÿ äëÿ ñòàòèñòè÷åñ- êèõ õàðàêòåðèñòèê îöåíîê ñïåêòðàëüíîé ïëîòíîñòè ìîùíîñòè ïðè àïïàðàòóðíîì ñïåêòðàëüíîì àíàëèçå ñëó÷àéíûõ ñèãíàëîâ íà îñíîâå ìåòîäà ïåðåìíîæåíèÿ ñ èñïîëüçîâàíèåì äèíàìè÷åñêèõ óçêîïîëîñíûõ ôèëüòðîâ. Ñóòü ìåòîäà ïåðåìíîæåíèÿ äëÿ àïïàðàòóðíîãî ñïåêòðàëüíîãî àíàëè- çà ñëó÷àéíûõ ñèãíàëîâ è åãî ïðåèìóùåñòâà ïî ñðàâíåíèþ ñ äðóãèìè ìåòîäàìè àíàëèçà ðàñêðûòû â [1,2].  [3] ïîëó÷åíû èñõîäíûå ñîîòíî- øåíèÿ äëÿ îïòèìàëüíîãî ñèíòåçà äèíàìè÷åñêèõ (íåñòàöèîíàðíûõ) óç- êîïîëîñíûõ ôèëüòðîâ, èñïîëüçóåìûõ ïðè îïðåäåëåíèè îöåíêè ñïåêò- ðàëüíîé ïëîòíîñòè ìîùíîñòè (ÑÏÌ) ìåòîäîì ïåðåìíîæåíèÿ. Ê ýòèì ñîîòíîøåíèÿì îòíîñÿòñÿ: à) ôóíêöèÿ ñïåêòðàëüíîãî îêíà èëè “ âåñîâàÿ ” ôóíêöèÿ ñïåêòðàëü- íîé ïëîòíîñòè ìîùíîñòè:            d cos H T 0 , (1) ãäå     dt t , t h H T       (2) – âûäåëÿþùàÿ ôóíêöèÿ èëè êîððåëÿöèîííîå îêíî; á) âûðàæåíèå äëÿ îòíîñèòåëüíîé äèñïåðñèè îöåíêè ÑÏÌ: ) 0 ( H I G ˆ 2   , (3) çäåñü    T 0 t 0 2 ) u , t ( h du dt I ; (4)     dt t , t h 0 H T 0   , (5) ãäå h(t,u) – èìïóëüñíàÿ õàðàêòåðèñòèêà äèíàìè÷åñêîãî óçêîïîëîñíîãî ôèëüòðà; Ò – âðåìÿ àíàëèçà. 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(11)  ñîîòíîøåíèè (11) ââåäåì îáîçíà÷åíèå                 d e ) , t ( h e ) , t ( h d ) t , W( 0 ) t ( j t 0 ) t ( j . (12) Î÷åâèäíî, W(  t) ïðåäñòàâëÿåò ñîáîé ïåðåäàòî÷íóþ ôóíêöèþ äèíà- ìè÷åñêîãî óçêîïîëîñíîãî ôèëüòðà âòîðîãî ïîðÿäêà. Ñ ó÷åòîì ðàâåíñòâà (12) ôîðìóëû (11) è (10) ïðèíèìàþò ñîîòâåò- ñòâåííî âèä:          T 0 1 dt t , W ; (13)          T 0 dt t , W Re . (14) Âû÷èñëèì ïåðâóþ è âòîðóþ ïðîèçâîäíûå ïî âðåìåíè ïåðåäàòî÷íîé ôóíêöèè W  ,t) äèíàìè÷åñêîãî ôèëüòðà âòîðîãî ïîðÿäêà, îïðåäåëÿå- ìûå âûðàæåíèåì (12): ) t , W( j d e ) , t ( h ) t , ( W 0 ) t ( j               ; (15)   ). t , ( W j ) t , W( j ) t , ( W j d e ) , t ( h ) t , ( W 0 ) t ( j                          (16) Óìíîæàÿ äèôôåðåíöèàëüíîå óðàâíåíèå (7) íà ) t ( j e    è èíòåãðèðóÿ ïîëó÷åííîå óðàâíåíèå ïî  , ñ ó÷åòîì ðàâåíñòâ (12), (15) è (16) èìååì                 ) t ( B j ) t ( A t , W t j 2 t t , W j t 2 t , W 2 2 0                     . (17) Ðåøåíèå äèôôåðåíöèàëüíîãî óðàâíåíèÿ âòîðîãî ïîðÿäêà (17) ñîñòî- èò èç äâóõ ñëàãàåìûõ: – “ óñòàíîâèâøåãîñÿ ” , êîòîðîå îïèñûâàåòñÿ âûðàæåíèåì       t j 2 t ) t ( B j ) t ( A t , W 2 2 0          ; (18) +x{lTUvyhV!bF$J@リML` D%*(ۦR "*({{Xwk5M&3wι|3' RD.FD*ۊpr""N1Og`<_3Hz;7Mo䱍:xG^S!'KT!#\7CE_Dn@nt{KnEˋ=AVRJs[/8dK}|vn)퐃g'9d{LtdQj N! gI@FKGv?9Yxc<20X+_2 Yp/U&rr !Z7M'F+ Dw:J渔\NP>e,*1tL aST?1xq5_"ΉRMk6q2N]jML_a$.ƿ>_E36,>y;ؐ&?os8NGg}xn?: B>O 7.h3%|H2~H1N2nԚE~\yxb^]Io׉og }5Sj\>X#Ά6 <K^ _'Wv2lF}ͯ>I[{zy궂8kYSjzֳPN5#X+;יJΗ]$; ^MF"1ħT켹s012NbO/]feLC{+ؓ%S36}y#+r[bӗGn:'cr`sfqV?57R2=cDg^]u#cb.(A)E[س>{{Ebp;Z_K=)B~L_~Q_se>Z}'pGŮާG3 JtO\!ߍ Q$.]X6.cuϵ﷒͍v\fsO\6IL %|ODϢ_4޾˼W9i!)940*%j{=I$H"Dh?p\_ $q}{8tHuIt' +M&`{XkH֯YL}i:Sr9MWx@c/\~OB]6 ָ8,ҥu6kk*d# \2ˡcl 1^x1RʜjBfE)flMqpK1ӸQOH95'8a~o5ۻa-ORV,$g⛈, Fb?"-)'C|nsqw݁ ~2|t,zuvI)p\86.&?x?D_%c-e4wFr ѕRmQ>ɶ=.|g{߶kīj/yIM5mO8K=NrQN3Fޙc=[1ݚ|$H"D࿁$h}w[.q  F ^)LT(16\2/ 1N8{x]E[m؉  {H! 6GdLF #Ȩg] *`>2+h 4!2dy}r{;Iu[uT9N:Ue Cg 2N ZN}Sma!l~I/U~` B gz֖&Q3_^l07|0, CEa~5E\! ٽk/J`=TnowuIu R8BxnQ2K!UW( .B[YSգe M]+Зm۶}{,EJT/tWQ'K-?cб^KC1`wp~303iAB_=  \ͅ}WX7qA"?C&q g*ޯkAW~Ǚ}=x`\ܬ?Q8ᑾ⋔wEѥ+me;7t6 B<ݗWTcꆧ.LBoriIY cG!x}ÅOޫ$ԅ rUDVz*ImV:4>ҖzH'Rl6vdbyYWClxlDW+ y*l#1ل+/I&n * Miy9RՏR7 8W'y<*m;DX5a>P E:ۤ0J)O*AlJJ a~ Wēcy 61)4'gça);1c+=Gy)TTұ+m%KJu_1y]vs&FMd81Iuܿf cxߥ2 v<~=ĔˎRx d6õr^ !脍ok-oUwiy90֦ÇmnU$ߩw }Zّ,ʏʃA,/6BϴѲ&B{`}u J龩 mJ3 yFcu )oQ;ƪׄ"Fcɶ{_lӪd@OGNݓdzȗe~:$~X?lFĺrmbֿ+ re9Kt{~|&К]!qN˵/ j_ .-Ϫ&˞ρރ ،3%s$ =|ΔẒ?ˍ9lzϯEU_T9?L^W'vso?Y;_y4ؿR~_)Wq*_ow+Wl_Lͯt|}rw_"a_VA]5hCģQΏ/z9.<.oӚKٻdzƒrޥ<<}`l]鲝ۏfyp2>37nhwK'Y{tl(ͫ9|iA[fq ;]6>5^<5/K}/\?{‘8Cq5dO՛EevIox4zrHMƒz`rʽgĸஶqm=b;͔-7CpwkD"I OS}Di)M -j.'|^D5dupwy;#5w8&g#w2t8ߏq9pBHǻ~<3_ԓw~hp9[fR}gd//h2k)jD0x;nR5G}^>#KiSOE'u(|*eڞy7( ~5Dc ڛ񿳷K^{!Κޣ~5GTZ`c}WywFG]c[+{knJv$=Uc6$@mLvbZ'ܤ,pOU v7i0 TbHn{ð9I 4!{6RYٱ=@{A:؟=ܤ^h6 >K7\[WH/J>۔EdG7Nj$O Mi+@/Ckq2MܩeLҷ3oU6o+dFdM\-6LPѤ"VEXAuF1}Ey~_> 'E[$ym:/U ?[; 3^+Fdtd x,X/Y692J{Vz)}N;GH<[is} {zi-LPhvG駍+h&g_Fo=xGȮ=Wwg A/[:u|pltvz^bsMV/ca;{ k[{+TFcxw]|NW͙${]bw4oXhۧ3P{h/="g_|M DǮ .'fkm+"^SƗaJ3^VzTQk'SucOٻjO`e 'w)fd3`]V' &KuݲYi3wubcطZmfKaM݀m݀M3`z81/˾r`$qc>yz@ݛ O݆݆E-1bʲG+(^`L63ܔ/pOlO!z8~k_rNdoIL2ȩF@[ɷN^e>oNA;WĊ%W_;sެAI8izӷPF"ƷBӍ_^k_G7=y쳗s vd5watiRR!o+ |\*;,UՓWc}[7E'Tkj'{\oU%c^oP*CK {)s,zӴX Ǒ ~{>nU#yW_}a#V]K+l'9o;ژW jcho?T'Uubd=$t[#TTu։$S3g<|Omr? 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Åñëè ñ÷èòàòü   t 1  <>1, òî “ ïåðåõîäíîé ” ñîñòàâ- ëÿþùåé ðåøåíèÿ óðàâíåíèÿ (17) ìîæíî ïðåíåáðå÷ü.  ýòîì ñëó- ÷àå, ïîäñòàâëÿÿ ñîîòíîøåíèå (18) â ôîðìóëó (14), ïîëó÷àåì äëÿ ôóíêöèè ñïåêòðàëüíîãî îêíà:                  T 0 2 2 0 dt t j 2 t ) t ( B j ) t ( A Re . (19) Èç ýòîãî âûðàæåíèÿ ñëåäóåò, ÷òî ïðè ìåäëåííîì èçìåíåíèè ïàðàìåò- ðîâ ôèëüòðà ôóíêöèÿ Ô(  ïîëó÷àåòñÿ óñðåäíåíèåì âî âðåìåíè “ çàìîðî- æåííîé ” ïåðåäàòî÷íîé ôóíêöèè ) t , ( W  äèíàìè÷åñêîãî ôèëüòðà âòîðîãî ïîðÿäêà. Ïåðåõîäèì ê îïðåäåëåíèþ îòíîñèòåëüíîé äèñïåðñèè îöåíêè ÑÏÌ G ˆ  ñîãëàñíî âûðàæåíèþ (3), äëÿ ÷åãî íåîáõîäèìî âû÷èñëèòü ôóíêöèè ² è Í 2 (0). Ôóíêöèþ ² â ñîîòâåòñòâèè ñ ñîîòíîøåíèåì (4) ïðåäñòàâèì ñëåäóþ- ùèì îáðàçîì:   T 0 dt ) t ( i I , (20) ãäå          t 0 0 2 2 d ) , t ( h d ) , t ( h ) t ( i . (21) Íàéäåì ôóíêöèþ i(t). Äëÿ ýòîãî èç ñîîòíîøåíèÿ (12) çàïèøåì             . d e , t h d d e , t h , t h d d d d t , W j 0 2 j 0 2                                             (22) Òàê êàê                     2 d e j , òî âûðàæåíèå (22) ïðåîáðàçóåì ê âèäó                 d , t h 2 d t , W 0 2 2 . 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G .xoW`qQp 48s.,z] ڥgF& XLjVvK2Bc[mSC1j K$m_3oJgZ #j82|kSMӳ>M:pL;4 CIu(m1.>'=E^ؒdkMrW []R (7 Xk͕ra:5/E/?Xw?Ź 2Ƌ!yXweJ\z2Ȑ9,CʐagQX"wSħu#=32d46bW ?ulf\SFܡ; W,P5C.XʆVYckOA9{8yUƛmټ^\I8e`ykGە6.|z"1Qtʰx'#ϝ|Jk ,S)7A{|gҫM,oe 2!,g,s`=@VCꙎ\8v@=ۇ}m}.O9iMy !@]WX"R15t=E 7Ϩ,^ųzaz13ѱ|ڕz~8`s|kFNu)/z\42BV?ASYVkTRZL>uۀm0^F߁Wj l:\W2eI{jyc2rl`FR[X>9,Տ5* ،I7 {.[~[TxFǜ;{\ GttE!<8b߃SCMx6S:vp}lu! -hf~HSFHKp%)5tID)]BG4Ӳ}PM:Ey~;rI=7vmq?sR,c*c?3ګ97p ׾()?5{Ĺםw6ΰ ضH~:KL96]CmP"@u]t{'a1=g=7t}!u5n/ vpSGeXy#KOx.AK͜c{yG ,mdNeB]` :v|sČ٧0h@;ƁeΜypr"i TA"XJ/׫l} l[ǺogTqҜy$|rlvnrbg@N#oۥqˠVrifcX KK2ʅRk}6j|a,Z YR0Nqs;F׋66##rOcpIuۭW]uXZ&b?N)L2 LQY>겒aޠpwj?cE_]c58clݾe99r#gGzP-_|J ;)\x~@e-;{HG׋YzӀ~!)uggЖ{E͍G4Q3Mg?-'d i+(ʨue2p胏=y%n훞quz`l-zn5t1W?>@i\O &6QǕߩ'kmZ0dj{ƫ-9FNY.Lvݲ P(kW(ף oSC@7m-!ߔ >+Oyʰc|[Ya3Yy~30%>S y3}DFNt̛.8t)cFPG)&{Oq`^b+O)Y`# Q3<_ %_~On_WtaL4*mW6#d sAqq +G6|XGz# cXf.s-N\̶ecɓ1iՍmd`X/w@72+brgc|I,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:46 35 Ïîñëå âû÷èñëåíèÿ èíòåãðàëà â ýòîé ôîðìóëå ïîëó÷èì   . 4 B A t i 2 0 2 2 0 2     Ñ ó÷åòîì äàííîãî âûðàæåíèÿ ôîðìóëà (20) ïðèõîäèò ê âèäó           dt t t t B t t A 4 1 I T 0 2 0 2 2 0 2       . (24) Íà îñíîâàíèè ñîîòíîøåíèé (5) è (9) èìååì       T 0 dt t B 0 H . (25) Ïîäñòàâèâ (24) è (25) â ôîðìóëó (3), ïîëó÷èì âûðàæåíèå äëÿ îòíîñèòåëüíîé äèñïåðñèè îöåíêè ÑÏÌ, êîòîðàÿ íàõîäèòñÿ ìåòîäîì ïåðåìíîæåíèÿ ñ èñïîëüçîâàíèåì äèíàìè÷åñêîãî óçêîïîëîñíîãî ôèëüò- ðà âòîðîãî ïîðÿäêà:             dt t t t B t t A dt t B 4 1 G ˆ T 0 2 0 2 2 0 2 2 T 0               . (26) Òàêèì îáðàçîì, ïîëó÷åíû èñõîäíûå ôîðìóëû (19) è (26) äëÿ ñèíòåçà îïòèìàëüíîãî äèíàìè÷åñêîãî óçêîïîëîñíîãî ôèëüòðà âòîðîãî ïîðÿäêà, èñïîëüçóåìîãî ïðè àïïàðàòóðíîì àíàëèçå ÑÏÌ ñëó÷àéíûõ ñèãíàëîâ ìåòîäîì ïåðåìíîæåíèÿ. Ñïèñîê ëèòåðàòóðû: 1. Òèùåíêî Â.À., ×èíêîâ Â.Í. Ïðèâåäåíèå àïïàðàòíûõ ìåòîäîâ îöåíêè ñïåêòðàëüíîé ïëîòíîñòè ìîùíîñòè ê îáîáùåííîé ìàòåìà- òè÷åñêîé ìîäåëè //Èíôîðìàöèîííûå òåõíîëîãèè: íàóêà, òåõíèêà, òåõíîëî- ãèÿ, îáðàçîâàíèå, çäîðîâüå: Ñáîðíèê íàó÷íûõ òðóäîâ ÕÃÏÓ.  ÷åòûðåõ ÷àñòÿõ. ×. 1. Âûï. 6. Õàðüêîâ: Õàðüê. ãîñ. ïîëèòåõí. óí-ò, 1998. Ñ.446-451. 2. ×èíêîâ Â.Í., Òèùåíêî Â.À., Õàð÷åíêî À.Ë. Ìåòîä èçìåðåíèÿ ñïåêòðàëüíîé ïëîòíîñòè ìîùíîñòè ñëó÷àéíûõ ñèãíàëîâ, îñíîâàííûé íà óñðåäíåíèè ïðî- èçâåäåíèÿ èñõîäíîãî ñèãíàëà è åãî ôèëüòðîâàííîé ðåàëèçàöèè // Âåñòíèê ÕÃÏÓ. 1998. Âûï. 21. Ñ.115-118. 3. Õàð÷åíêî À.Ë., ×èíêîâ Â.Í. Èñõîäíûå ñîîòíîøåíèÿ äëÿ îïòèìàëüíîãî ñèíòåçà óçêîïîëîñíûõ íåñòàöèîíàðíûõ ôèëü- òðîâ ïðè ñïåêòðàëüíîì àíàëèçå ñòàöèîíàðíûõ ñëó÷àéíûõ ñèãíàëîâ ìåòîäîì ïåðåìíîæåíèÿ // Âåñòíèê ÕÃÏÓ. 1999. Âûï. 24. Ñ.52-57. Ïîñòóïèëà â ðåäêîëëåãèþ 12.11.99 Õàð÷åíêî Àëåêñàíäðà Ëåîíèäîâíà, ñò. ïðåïîäàâàòåëü ÕÃÏÓ. Àä- ðåñ: Óêðàèíà, 61176, Õàðüêîâ, óë.Êîð÷àãèíöåâ, 36, êâ. 65, òåë 40- 00-83. ×èíêîâ Âèêòîð Íèêîëàåâè÷, ä-ð òåõí. íàóê, ïðîôåññîð ÕÂÓ. Àäðåñ: Óêðàèíà, 61202, Õàðüêîâ, óë. 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Ïîò³ì âèçíà÷àºòüñÿ, ÷è â³äïîâ³äຠîòðèìàíèé ðåçóëüòàò ( “ íàñë³äîê ” ) ïî÷àòêîâ³é ³íôîðìàö³¿ ( “ ïðè÷èíà ” ), òîáòî “ íà- ñë³äîê ” ïîâèíåí â³äïîâ³äàòè “ ïðè÷èí³ ” . Âèçíà÷åííÿ â³äïîâ³äíîñò³ ìîæ- ëèâå øëÿõîì çâîðîòíîãî ïåðåòâîðåííÿ ðåçóëüòàòó ç ìåòîþ îòðèìàííÿ ³íôîðìàö³¿, ÿêà ïîð³âíþºòüñÿ ç ïî÷àòêîâîþ ³íôîðìàö³ºþ. Ïîâíèé çá³ã ñâ³ä÷èòü ïðî â³äñóòí³ñòü ïîìèëîê, à íåçá³ã ãîâîðèòü ïðî ¿õ íàÿâí³ñòü. Ïðàêòè÷íà ðåàë³çàö³ÿ öüîãî ïðèíöèïó äëÿ êëàñè÷íèõ àâòîìàò³â ç ïàì ’ ÿòòþ ³ êîìá³íàö³éíèõ ñõåì äîñòàòíüî ñêëàäíà. Ïðè÷èíîþ ö³º¿ ñêëàäíîñò³ º òå, ùî âîíî ³ ïîð³âíÿííÿ çä³éñíþþòüñÿ íàä áàãàòîðîçðÿä- íîþ ³íôîðìàö³ºþ. Äàíîãî íåäîë³êó íåìຠïðè ôóíêö³îíàëüíîìó êîíò- ðîë³ áàçîâèõ ì³êðîîïåðàö³é, îñê³ëüêè âîíè âèêîíóþòüñÿ íàä ìàëîþ ê³ëüê³ñòþ ðîçðÿä³â êîäó. ̳êðîîïåðàö³¿ çãîðòêè ³ ðîçãîðòêè, çíàêîâî¿ çãîðòêè ³ çíàêîâî¿ ðîçãîðòêè º âçàºìîçâîðîòíèìè. Öÿ âëàñòèâ³ñòü ëåæèòü â îñíîâ³ ¿õ êîíòðîëþ çà ïðèíöèïîì çâîðîò- íîãî ïåðåòâîðåííÿ, àëå çâîðîòíå ïåðåòâîðåííÿ íå ñïåö³àëüíà êîíòðîëþ- þ÷à îïåðàö³ÿ, à îñíîâíà. Íàïðèêëàä, ïðè âèêîíàíí³ çãîðòêè íàä êîìá³íàö³ºþ 011 ( “ ïðè÷èíà ” ) îòðèìàºìî êîäîâó êîìá³íàö³þ 100 ( “ íà- ñë³äîê ” ), ÿêà º íåîáõ³äíîþ óìîâîþ äëÿ âèêîíàííÿ ðîçãîðòêè, òîáòî ï³ñëÿ ïðàâèëüíîãî âèêîíàííÿ çãîðòêè îáîâ ’ ÿçêîâî âèíèêຠóìîâà ìîæëèâîñò³ ðîçãîðòêè. Àíàëîã³÷íî, ïðè ïðàâèëüíî âèêîíàí³é ðîçãîðòö³ âèíèêຠóìîâà âèêîíàííÿ çãîðòêè. ßêùî ïðè âèêîíàíí³ çãîðòêè àáî ðîçãîðòêè óòâîðþþòüñÿ êîìá³íàö³¿ 000, 001, 010, 111, 110, 101, òî öå º ðåçóëüòàò ¿õ íåïðàâèëüíîãî âèêîíàííÿ. Îçíàêîþ ïðàâèëüíîãî âèêî- íàííÿ ì³êðîîïåðàö³¿ ïåðåì³ùåííÿ  1 0 º îòðèìàííÿ êîìá³íàö³¿ 0 1 . Êîìá³íàö³¿ 0 0 ³ 1 1 – ïîìèëêîâ³. ̳êðîîïåðàö³ÿ ïîãëèíàííÿ 1 1 ââàæàºòüñÿ âèêîíàíîþ ïðàâèëüíî, ÿêùî îòðèìàíà êîìá³íàö³ÿ 0 0 , ³ íåïðàâèëüíî âèêîíàíîþ ïðè îòðèìàíí³ êîìá³íàö³é 0 1 ³ 1 0 . Îòæå, ò³ êîìá³íàö³¿, ÿê³ º äîçâîëåíèìè äëÿ ïåðåì³ùåííÿ, º çàáîðî- íåíèìè äëÿ ïîãëèíàííÿ, ³ íàâïàêè. ßêùî ïðîàíàë³çóâàòè “ ïðè÷èíè ” ³ “ íàñë³äêè ” ì³êðîîïåðàö³é, òî ïðèéäåìî äî âèñíîâêó, ùî “ íàñë³äîê ” º ³íâåðñ³ºþ “ ïðè÷èíè ” , òîáòî óñ³ ì³êðîîïåðàö³¿ ìîæóòü áóòè çâåäåí³ äî ³íâåðòóâàííÿ ðîçðÿä³â ïðè âèêîíàíí³ â³äïîâ³äíèõ óìîâ. Íà ðèñóíêó íàâåäåíà ñòðóêòóðíà ñõåìà ïðèñòðîþ, â ÿêîìó çä³éñíþºòü- ñÿ ôóíêö³îíàëüíèé êîíòðîëü çà ïðèíöèïîì “ ïðè÷èíà-íàñë³äîê ” . Êîä, ùî çíàõîäèòüñÿ â ³íôîðìàö³éíîìó ðåã³ñòð³, àíàë³çóºòüñÿ ëîã³÷íîþ ñõåìîþ “ ïðè÷èíà ” . 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(,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:46 38 ðîçðÿä³â â ³íôîðìàö³éíîìó ðåã³ñòð³ ëîã³÷íà ñõåìà “ íàñë³äîê ” àíàë³çóº âì³ñò öüîãî ðåã³ñòðó òà ñêèäຠ⠓ 0 ” ò³ ðîçðÿäè êîíòðîëüíîãî ðåã³ñòðó, ÿê³ â³äïîâ³äàþòü ðåçóëüòàòó ïðàâèëüíî âèêîíàíî¿ ì³êðîîïåðàö³¿. Íàÿâí³ñòü ï³ñëÿ öüîãî â êîíòðîëüíîìó ðåã³ñòð³ íóëüîâîãî êîäó ñâ³ä÷èòü ïðî â³äñóòí³ñòü ïîõèáîê. Ïðè íàÿâíîñò³ õî÷ áè îäí³º¿ îäèíèö³ â êîíòðîëüíîìó ðåã³ñòð³ ôîðìóºòüñÿ ñèãíàë “ ïîõèáêà ” , òîáòî êîíòðîëüíèé ðåã³ñòð âèêîíóº ôóíê- ö³þ âñòàíîâëåííÿ â³äïîâ³äíîñò³ “ ïðè÷èíè ” “ íàñë³äêó ” . Контрольний регістр Логічна схема “ причина ” Логічна схема “ наслідок ” Інформаційний регістр помилка вх. вих. Ñòðóêòóðíà ñõåìà ïðèñòðîþ ç ôóíêö³îíàëüíèì êîíòðîëåì Íà îñíîâ³ îïèñàíî¿ ñòðóêòóðè ñàìîêîíòðîëþþ÷îãî ïðèñòðîþ âèäíî, ùî ðåàë³çàö³ÿ áàçîâî¿ ì³êðîîïåðàö³¿ ó ÷àñ³ â³äáóâàºòüñÿ çà òðè òàêòè.  ïåðøîìó òàêò³ ñ 1 ³íôîðìàö³ÿ, ùî ñôîðìîâàíà ëîã³÷íîþ ñõåìîþ “ ïðè÷è- íà ” , çàïèñóºòüñÿ â êîíòðîëüíèé ðåã³ñòð. Ó äðóãîìó òàêò³ ñ 2 çì³íþºòüñÿ ñòàí ³íôîðìàö³éíîãî ðåã³ñòðó ï³ä 䳺þ êîäó, ÿêèé çíàõîäèòüñÿ â êîíò- ðîëüíîìó ðåã³ñòð³.  òðåòüîìó òàêò³ ñ 3 ëîã³÷íà ñõåìà “ íàñë³äîê ” çàáåçïå- ÷óº óñòàíîâêó â íóëüîâèé ñòàí âèçíà÷åíèõ ðîçðÿä³â êîíòðîëüíîãî ðåã³- ñòðó. Íà çàâåðøåíí³ òðåòüîãî òàêòó ôîðìóºòüñÿ ñèãíàë “ ïîõèáêà ” . Ïðîàíàë³çóºìî çäàòíîñò³ ùîäî çíàõîäæåííÿ ïîìèëîê êîíòðîëþ çà ïðèíöèïîì “ ïðè÷èíà-íàñë³äîê ” . Äæåðåëàìè ïîìèëîê ïðè âèêîíàíí³ ì³êðîîïåðàö³é º: – çáî¿ ïðè ïåðåìèêàíí³ òðèãåð³â; – çáî¿ òðèãåð³â, ÿê³ íå ïåðåìèêàþòüñÿ; – â³äìîâè åëåìåíò³â. ßêùî çá³é âèíèêຠïðè ïåðåìèêàíí³ êîíòðîëüíîãî òðèãåðà â ïåð- øîìó òàêò³, òî ì³êðîîïåðàö³ÿ â äàí³é ãðóï³ ðîçðÿä³â íå áóäå âèêîíàíà. Ï Â Â 2x]lSuƟu[isa.qa\YG%1 4 *EAnqF(LV.3  ~ ^]{=vz9ɓx$vI7J1\Nnv~\r*lSqi=Y =|[ϥFDQ5j t AVf*?E:Ok&qխêqW7ݥ\FXj5kuҫQY'<|6/z\3Hδ\,\ݗ#'t"CL7uȝ7ٚ5hMUfm%ګgUa>_J講/|ls&lB;ˈ~_=g*k 糜gѫi߮xAbND)o{Gڷ򵬘8-9dQ&zM\,e8˝fٹV5\Ɍq pY9mK3n9N '0j;C~4rM먽Ӡ 1j>2W=| > ؇nf%^%k^Ac{5N(}cf-A7:iKYf6Gқaަf 9$Ç^4gov#^n˩9L;aߎ`AEKy{N'3ɽցN]NwP>4ם 8ic4;*fu|M1 ?g`IVԻ.^[(_.WwϕL_d"c}cI_T>W:_~>\i^֔)JR}KBRRr}Zأ73 `v ؁`g9v ؁` %'    #  (16 2 /  1V :Z {hxUu矉0bL@(xfL a#o`L#jԩ&[!qhSDE7miam?jwi-Ya)V #H5B]~tH„$wy3yɽss;/-I1!INIA;`Q~J .|W$5If.I $,[s`$Qvr\K̃SOy]rɧT,!q%kjH#JSCTGqCv+9Jpr utg R4u-e-Oס荂ׯ `2%KRKBH5;?Fj7K<Ic _9mj-o̕I25oõmK~~tytOICC }[(`/l)nHz;Onoq]xd>ҖFodrZ\a65sjQFQE[Vה!ebRHd[EzVڜ ̠b 6fR۔l,E *(4Pm! +P'#yAo.y4?q\8_%+8A(CnAk2yRަ6$wJuK{^ efҬL?;t?8rt<Χ2>f K(.QYȠ}V%GrmQwhެ'fe2i^>'`gɣCֈȖ4uڴ :=.d^6Nm`"TF)o%r7(Y`l:]RۦI;Wj+]ީ8^tKNA\G(읢r 4<'}>#𸜬8〴2E oDig:G%g].i6vP7qS7t :iCy3r}//7H4Z礙#U  =m*ŨWmwf@3ߩ ] F$Α 2I[ 43-qv@y|dl]턐kC,@gnBk>)t|IئyS\`cKuw t}pD;_a=8^7蒹y@Q.儙w K5M#2#l,+Xoi ?}Q8^oeį? 8Y_ʒ}.,=N$5mVni.+05YF? 7ˏ~&SiHGNv424SG:bP8uLpt;ob^2nwpGJg tG\ʛ|%P2mbA^K륞0Yk{UT-׍f;ºYk ,->x[O sOKʬw81ӳG?coxc'3M !F=COO>C!xp:)O0ؓ1Gm^lm#mn,uCi%xX}{:uɛ"ܹ-1k@/tܦl-zs!a%SNin [2xZ셵oV<l1[%?K_Nei}0C.@vк uD8/feGRu ux@tc# L)%zp =Gm+/<JMl:ݓz1iCT666 d̯GC&)҄Ȗ5e-O䙏CG=q{NƓ'ĩ>li4g|xU t|p#Ngb?NtC~@6l"G&G Խrq;5y!;e9L(ΐid,;ò>rʺiE{9umٞk}CӞ>Yk[IW/T̥A5&QܦQYa.e6t_MzM<dL-FI[q-ob!yPZW.*nyz=oNtI> M=HZt\]2nh r[<#ac+9Q8}_ dlnӿ(蔼?|іtŹOk&#`8.(gJVXXH},Egͽ1Szt Iێ-Say?bNFD[mu̳[8p?m:C{蛽!4D.8 y[2n/cz ?KY:BxЛ#u /?wOS ??'\ğ`wR8 :e\sS,vɛ;.<06xD?/2螺e<->Z0& xtAY1ChxsE۞ɃAk1O7. %ݯp*5\87}ON(cieb{^ۀ7y=e*:bȣssa i N-e 56S5oY~el߃G ;<6GB~<@cݚ][}POC<"u`cЀ\6QtG]?w 5ۤ+x@!v 7_Ɓ{+^s/ rOƭ~kvy<§;WV^Mםų*|Z l7@>#d< lɣuh9p]p}ԑ ȷ]QZBtbeQt\n킮KpN/{pe:Wkmvo[3 [>S1.cq>=Xb Of3G8-c;z圵Rȩ%foۉmٲܑe =s冼!; @6#y -qp]7!u':t}y!N]pnx1 ez.w i6* =gxo z^E_3m|Џ!tDofhٵ ݂ L}~L=asn RE“[Mab.Ǔl. /U9! i:<̐cl;e: r*z[$X!yI$ +o|7qpxޢ8U8ܻmB;Z,M x!,{w;w|x)}?Ȗ ~*@_C[/I•5{T>yٌ+釾ۤl`pNJ*/`,MCqAe; X#.(SCOkgʁG' p$CXPy¡ѕu |]?6A݋uB~_ :DCO bI^AFy;Gv':Z(E̼(۲୲Jx*;ʫI$"Бu:s4~|9!io]kYa'_IɃz\ros"娇.,u %h7lNmQhcωR8 D85`&d_&#&Sk#>ȉE,tF^g SbYX#/d< =xEhc)(gmi.n_N3tAއLKW?g5y}sqiu ؑ}s \v6yGdRG]!W%*xU?y?Ke]yvX; jUGm7wf+_G,d;Bvzȳl41M44m+"4o[K@G=|R[ %!~&Xɖe 6{WϬ۶N h}#X4̳4]߄ve{dpYBs !zNB/ gIcLaR^e=./3|uNɐ][G:хi'q7=e}n5 n*;;O=w ^ h#@-;Dm0j:N#bxp3㭳7We7GkVgu*`, f(ɳ=v*SqJ{Oi=eϿSh׶NH&di^rO'˿-_qz|op S{d(h/&ݢk_)egTu;k<_|嗧$w rgqSF B]Sپw1AZ[Ad^4,P}ɅCNKWR;W}G66/?49E}|Tu;{$;5-`ie DZAsAx{tn\AHdI>ծ4@#5yQG0b}}G/z*ʳ^ (+tko['hfu5jN6^nj=&=lvcTO𥞅bcto|@e-uפQ8Uc~z>sWwPn⌽{_1XzE ʨ\o*juxj>h&t>a3鑾Hqx&naZ_s"}F~SqK^k,}o}.?$lF_U6^ IR!n?}MKnR}/ڥ5}Q._GWu#ғ:uvNh,.h Xl=9/1Y_j[2aB=L^s_{^߱hK4W6_H-G$>HrI{A#>\~q!xOsϩ:@{7bS>3&ok/|QB!M=~5o6ecu6~!B {`~pu!t=CT˂IT&{RŎd²'V+E pVftxGƩ'"cB{Gx>[-ީ9ҝᗟ;YYȔ8,H#/҄}KZqX:Zp!uOBpS}r]>Sgם^kPKCiWȔQ[R"ص)C>)0_ nV;TUi.xP,_"+Ý~Y??E1 2$X>:h\h'ho:nGʚƺ}'y7FG_.}Ck7;MmϽBW_zA1J&2~hxntʈ3K'q?  _:EYK]y'eJMuPhEYӸNƵ G;-a@>Pxc#ܹ•eIv i?P<.x*zHh]EM/9# X ?#m.u^%o 3"bzBjzd-/|Ay|ҿ :1¯wwCG oÊGa9TGğ.-l<fWvv Cq0[ ǂ?xta}{Q\nl+S7y?Pu^Sz|s`R߯iCo ph{z! dt3fL!!ڋ,mX8e'v ,l 'mNBqvCގ]+{9-zCzI5aK7-m' \ xgyHiī)~ g`&/>)_R3^boS:~ oₖkJԛ89)ڷM\ $q`Y٦nesDW~ⓟ4I\z?,^u+ȹej}`6Y蛷)9IBv|lfͅ6#_o/?m;>N߁QEχ[;)ÿ F_|a_x{z@ =| ߥƗBD/khjh'!oDs53峎 ;uq:3t:_-fJ%zNIE{r Nc"oAњo~|}m?qp0qtйbu]ۚ+kc 3]/?=}_H}o+ߒtf eN-UW<9lQ|ܥtv]GPz-7+9JFo()ђ}$2/2zm¢mYg#9v*Pֆ>vşn!r- [wP馣5s:uxQs`oe2[D?S0Z]_' %c!uͶ!>܆ؐuB[Dq&}Oqzc>ojNnQ1_}~`Ad&l>(ש>H7cݪL>:I}`csZOo=C)J<7qc^$`=5БɚY 6SSjxa&dN]:+346'c|A_өE[zҗ M&3xvZq ]Fj^m dMn8 5]4E؎mm$C3~_r_gho:6?#~h >N~7 3T{gH7g+sˋ6ba7mcy(݇Z%xc,k]ASnm`֙J;Y*;g%I1ۆʡڵL/y4]=hK+=k),e3}1ER ڴ[R=l `?7ӉڌTk;C'l_H[tlj?&}p&$raS>D:Qҭ:XC& a&-}To:_r]CC} AҶ45Zb,ZD، QS nƆ~&`mFy: :Cf0[/hnioZ ?!ֿ{>#8r>CN6BG,F6bd_l#g7#Z>{Ib7ẹQɾ{=W5hC-z&ei9#݇?&zV5G3A_5v쁅j˗~}}$63¥*63Zgҹ[9WzL=|gͶɯaU sk#5&5.%{T?nBm݂r~CJ{ʎDX0ڵs{ a\hE9L4Ќs^ cWv /\$8c()=ǐn\:X[_Δ]:'e/N՝wއaGr=ul=|\ 4.7ܿ멎aߏoWߞvi=/j#f™Bx0]Wzmcہom6_#syl\([y9LC#ޒ%?|(J}œ{~#{ 9?Wޜ]WrwKwGy:~SλO~~I>{f9NfQ!sԐA½cf_@A%zRH:&PMX=_q݊ߚZ~vkLKgfuhqypGite1s E/8n?Ueuvf{F)ӕZu՜]"u:agҟhTmMz,#*ڙu;>-WjN;҄_ѝss<]7_ٹ<6t]pb%Ptlpa[6-{~f ~9 ZgvE .U^cve{ءm{W6_~oAk[3l_Zyog.i]g F{W~/>+{OrVְ9~Chs/ߛS +soC{'Ѽ){?aUׂ÷NOcϟW?Q!燄W3ؗgCy(6<z~s oCy(8ޜsy(9wU~[s oCyhUޜx+7<ޜ»PxsVoj7>&ħ2_SV/}*gƯVo| -ƷTś3Ix37c ތ1x3ƪ͙$sxcwS՝rI lg7$ZN-|@6RQL:SV>u3gg3'jm$i8ODƼ-Y]җA$t[ǶLh{HjʍǞklXg|yy"c#{c>a(!=(%)=eg6ћ }.].a|J?čƴ}gz' x7i?M>ۆ~7eV*{[^/;߻ҧf ^7/*,Ik q]*>;aE^6os$r}}|{K67E`fZucu65l6gVmjx6WslϭHa3-Jjypfǽ.f-j/a/U$[g|Wooي>_]jWm v:Jql~dvw[oާsX\sXۂwUw[ ~kVEۂ7w[n~Wuo%sUn m-xWuoξwUn m͹;9w7U-xso]97gU|O=Ih'ؗ>Gsʛ~3o]\K7sIU.~Û~û*}3y cjCcȜy*sKM]̙C oPxW5"sPdZ̹Jf77sod̙9779kxv7kxWv@9kd[ o d^#D_ L(k{gι=u ȧT `9Jw*^2.g֦i=,(|TV,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:46O39 Ïðè çàïèñó êîäó öå ïðèçâîäèòü äî ïîìèëêè, ÿêà áóäå çíàéäåíà, à ïðè çñóâ³ êîäó òàêà ïîìèëêà íå âèÿâëÿºòüñÿ. ßêùî çãîðòêà, ðîçãîðòêà, ïåðå- ì³ùåííÿ ³ ïîãëèíàííÿ çàñòîñîâóþòüñÿ äëÿ ï³äñóìîâóâàííÿ àáî â³äí³ìàííÿ, òî ïîìèëêè â öüîìó âèïàäêó íå âèíèêàþòü ³ ì³êðîîïåðàö³ÿ â äàí³é ãðóï³ ðîçðÿä³â áóäå âèêîíàíà íà íàñòóïíèõ òàêòàõ. ßêùî çãîðòêà ³ ðîçãîðòêà çàñòîñîâóþòüñÿ äëÿ ë³÷áè îäèíèöü, à ïåðåì³ùåííÿ ³ ïîãëèíàííÿ – äëÿ âèêîíàííÿ ëîã³÷íèõ îïåðàö³é, òî âèíèêàþòü ïîìèëêè, ÿê³ íå çíàõîäÿòüñÿ. Âèíèêíåííÿ çáîþ ïðè ïåðåìèêàíí³ ³íôîðìàö³éíîãî òðèãåðà ó äðóãî- ìó òàêò³ àáî êîíòðîëüíîãî òðèãåðà ó òðåòüîìó òàêò³ çàâæäè ïðèçâîäèòü äî ïîìèëêè, ÿêà çíàõîäèòüñÿ. Âñ³ çáî¿ òðèãåð³â, ÿê³ íå ïåðåìèêàþòüñÿ ó âèçíà÷åíîìó òàêò³, òàêîæ ïðèçâîäÿòü äî ïîìèëîê, ÿê³ çíàõîäÿòüñÿ. ³äìîâè åëåìåíò³â ìîæóòü áóòè äâîõ òèï³â: ñòàëà “ 0 ” ³ ñòàëà “ 1 ” . Õàðàêòåð ïîìèëîê, äî ÿêèõ ïðèçâîäÿòü ö³ â³äìîâè, íàâåäåíî ó òàáëèö³. Ïðè âèêîíàíí³ ï³äñóìîâóâàííÿ ³ â³äí³ìàííÿ ³ñíóº îçíàêà çàê³í÷åííÿ îïåðàö³¿, ÿêà äîçâîëÿº äîäàòêîâî çíàõîäèòè ïîìèëêè, ùî ïîðîäæóþòüñÿ â³äìîâàìè ³ íå çíàõîäÿòüñÿ êîíòðîëåì çà ïðèíöèïîì “ ïðè÷èíà-íàñë³äîê ” . Äëÿ ï³äñóìîâóâàííÿ ³ â³äí³ìàííÿ â³äîìî ìàêñèìàëüíèé ÷àñ âèêîíàííÿ îïåðàö³¿, ³ ÿêùî çà öåé ÷àñ îïåðàö³ÿ íå çàê³í÷óºòüñÿ, òî öå ñâ³ä÷èòü ïðî íàÿâí³ñòü â³äìîâè. Àíàëîã³÷íà ñèòóàö³ÿ ìîæå âèíèêíóòè ïðè âèñîê³é ³íòåíñèâíîñò³ çáî¿â, ùî, ÿê ñâ³ä÷àòü åêñïåðèìåíòàëüí³ äàí³, â³äáóâàºòüñÿ ç åëåìåíòàìè ïåðåä ¿õ â³äìîâîþ, òîáòî º ìîæëèâ³ñòü ïåðåäáà÷àòè â³äìîâó. Ïîìèëêè, ùî çíàõîäÿòüñÿ, óêàçóþòüñÿ ç òî÷í³ñòþ äî p +2 ðîçðÿä³â, ùî äຠìîæëèâ³ñòü ââåñòè îö³íêó âàæëèâîñò³ ïîìèëîê ³ íå çóïèíÿòè ïðîöåñ îá÷èñëåíü, ÿêùî ïîìèëêà íå³ñòîòíà. Ïðè âåëèêèõ n éìîâ³ðí³ñòü ïðîïóñêó ïîìèëêè äëÿ óñ³õ ì³êðî- îïåðàö³é äîð³âíþº: n N N   2 заг незн , äå N íåçí – ê³ëüê³ñòü ïîìèëîê, ÿê³ íå çíàõîäÿòüñÿ; N çàã – çàãàëüíà ê³ëüê³ñòü ïîìèëîê. Ó ñó÷àñíèõ âèñîêîíàä³éíèõ îá÷èñëþâàëüíèõ ïðèñòðîÿõ íàé÷àñò³øå âèêîðèñòîâóºòüñÿ êîíòðîëü äóáëþâàííÿì, ÿêèé çàáåçïå÷óº òàêó æ éìîâ³ðí³ñòü ïðîïóñêó ïîìèëêè, àëå éîãî ðåàë³çàö³ÿ äëÿ “ ô³áîíà÷÷³º- âèõ ” áàçîâèõ âóçë³â ïîòðåáóº áëèçüêî â äâà ðàçè á³ëüøå àïàðàòóðíèõ âèòðàò ó ïîð³âíÿíí³ ç çàïðîïîíîâàíèì ñïîñîáîì êîíòðîëþ. Ðîçãëÿíåìî àïàðàòíó ðåàë³çàö³þ áàçîâèõ ì³êðîîïåðàö³é. Ïðè öüîìó áóäåìî ââàæàòè, ùî êîíòðîëüíèé ðåã³ñòð ðåàë³çóºòüñÿ íà RS-òðèãåðàõ, à ³íôîðìàö³éíèé – íà D-òðèãåðàõ. 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Äëÿ âèêîíàííÿ íàä ãðóïîþ ðîçðÿä³â êîäó ì³êðîîïåðàö³é çãîðòêè àáî ðîç- ãîðòêè íåîáõ³äíà íàÿâí³ñòü òàêèõ óìîâ, â³äïîâ³äíî: . , 1 * , 1 * , l p i k l k i i k i l p i k l k i i k i x x x g x x x f             Îäíàê öüîãî íåäîñòàòíüî ïðè p >1, îñê³ëüêè îäíà ³ òà æ îäèíèöÿ êîäó ìîæå áðàòè ó÷àñòü îäíî÷àñíî â äåê³ëüêîõ ì³êðîîïåðàö³ÿõ. Íàïðèêëàä, ïðè p =2 ³ k =1 îäèíèöÿ i -ãî ðîçðÿäó áåðå ó÷àñòü ó äâîõ çãîðòêàõ: i+3 i+2 i+1 i i-1 i-2 0 1 0 1 0 1 Äëÿ óñóíåííÿ íåîäíîçíà÷íîñò³ äîçâîëÿºòüñÿ ò³ëüêè îäíà ì³êðîîïåðàö³ÿ ó ãðóï³ ðîçðÿä³â, ùî ðîçãëÿäàþòüñÿ, à ³íø³ çàáîðîíÿþòüñÿ ââåäåííÿì âèçíà÷åíèõ ëîã³÷íèõ óìîâ. Òàê, â íàâåäåíîìó ïðèêëàä³ äîçâîëÿºòüñÿ çãîðòêà â ñòàðøèõ ðîçðÿäàõ: i -ìó, ( i +2)-ìó ³ ( i +3)-ìó ³ çàáîðîíÿºòüñÿ â ìîëîäøèõ ðîçðÿäàõ: ( i -2)-ìó , i -ìó ³ ( i +1)-ìó.  çàãàëüíîìó âèïàäêó, äëÿ áóäü-ÿêîãî p ìàºìî òàê³ ëîã³÷í³ óìîâè äëÿ âèêîíàííÿ ì³êðîîïåðàö³é çãîðòêè CV 1 ³ ðîçãîðòêè DV 1 , â³äïîâ³äíî:          ; 1 для , 1 для * 1 , * 1 , 2 1 p f f p x x x f p i i i i i i          . 1 для , 1 для * 1 , * 1 , 2 1 p g g p x x x g p i i i i i i Áàçîâèé âóçîë, â ÿêîìó âèêîíóºòüñÿ ì³êðîîïåðàö³ÿ çãîðòêè, áóäåìî íàçèâàòè ðåã³ñòðîì çãîðòêè .  öüîìó ðåã³ñòð³ i -é ðîçðÿä ëîã³÷íî¿ ñõåìè “ ïðè÷èíà ” îïèñóºòüñÿ âèðàçîì i i f c S 1  , à ëîã³÷íî¿ ñõåìè “ íàñë³äîê ” – âèðàçîì:       . 1 для ; 1 для * 1 , 3 3 p g c p g c R i i i Äëÿ ðåã³ñòðó ðîçãîðòêè â³äïîâ³äíî ìàºìî: i i g c S 1  ;       , 1 для ; 1 для * 1 , 3 3 p f c p f c R i i i à äëÿ ðåã³ñòðó çãîðòêè-ðîçãîðòêè – ) ( 2 1 1 i i i g y f y c S   ;         , 1 для ) ( ; 1 для ) ( * 1 , 2 * 1 , 1 3 2 1 3 p f y g y c p f y g y c R i i i i i äå 1 y – ñèãíàë, ÿêèé äîçâîëÿº çãîðòêó; 2 y – ñèãíàë, ÿêèé äîçâîëÿº ðîçãîðòêó. +x pT-$li0T%QU&鴔A@;ʷւX-) tHJmP壃`gb)R Ш`'7t:Vn?sϽ;q/\- ԁ% " )vb9""zyq{l M s{&F;2X  Uվ*$ם)Uw;|QRE" '[ɖl9߂w0YMz7K&vڻO׼kM~+oK 4w[ aER+ n_yԂ9.<'_ Ȩ@ǞDth[V~O`aSmWrQc }ʉp0p[PPM84 SNUoE>. 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I >мnTt#D(KdRwgyIٶ.<''İ  dwb{}wKzr=%Qlf?*ſlS۷fSȌ xߪ@?3>㔱'6\-Y[?ZT@͍ZSYGX<#/xeMSqlmP 읉UbƬ{FoV'>xo:7_9;YA iwhp}ck_G:?w9;O|pd\t$gΗ ۱=\8{M?>Tj틿[ mbhWm3~ϏQgݏWW/W_< r!>t!8tmw.!bڦ zs8Л+.MЛz#s'Sg?>UI>IEV{Coӽ/όF;4{pc[Ko'Y_d,i|N7JČߏjoQ/.໺|65CsGUruuo3*Զޣ|ܨUߥyQg|wͬ{*xveQ~4QXFhl0teAo+<^)'L|<|8]bh~ǒ}$ E+~~b ù3<ۯb]RC.ռnTǻCF Pa^HvG> : 񉁛\7ڄ u]z™֓W h./'e!{p۟ھ6ݣ:֬e*/*.)c?.܏OUY-:x{D*+'suǘ{'>(啅 M:tG]o]1`$9ѢH>lNG?C.;3$niIV_y~bt|X^-sR?$fMN3\~ab哓6ŋTvYVymKr|և<>9kǴ=Hm}vȟɜ}KLՀ9K`bh8&)&ܬ LxgdM.YäVT@-#+BBI5oMKν@ 5$ǀYp 9pU2e8_/v=Q%<=H[嫢dMЃ1k+Ւ1~L$|'J?*vs #o*nƵT2!TFVj\K"kH|=;$U/ 徠b :)m&ARbXz|oKYSdJ2s~_k'X=2b-\1p&P䉵a랩CM≗'4&^'[7( [*վ7:Bt M-cUK:ͯU_Cn3p,mט;u0bdVrOHf$%wSA=xd|%ݕ8Ns_U։ I~^>|45{ü F ZVe1pبUp{9x?7|8=;||&6SL^j!xs&T,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:4741 Ôóíêö³ÿ çáóäæåííÿ äëÿ i -ãî ðîçðÿäó ³íôîðìàö³éíîãî ðåã³ñòðà ìຠâèãëÿä: ) ( 1 p i i i i i T T T Q D       , äå i Q – âèõ³äíèé ñèãíàë i -ãî D-òðèãåðà; i T – âèõ³äíèé ñèãíàë i -ãî RS-òðèãåðà. Çãîðòêà 1 CV ³ ðîçãîðòêà 1 DV , ÿê âæå â³äì³÷àëîñü âèùå, îñíîâí³ ³ âèêîðèñòîâóþòüñÿ ïðè âèêîíàíí³ ï³äñóìîâóâàííÿ òà â³äí³ìàííÿ ïàðà- ëåëüíèõ êîä³â. Ïðè ï³äñóìîâóâàíí³ òà â³äí³ìàíí³ ïîñë³äîâíèõ êîä³â êð³ì öèõ ì³êðîîïåðàö³é âèêîðèñòîâóþòüñÿ çãîðòêè ³íøèõ âèä³â, òîáòî 2 CV , 3 CV , ... . Îñê³ëüêè äëÿ çîáðàæåííÿ ìàòåìàòè÷íèõ îá ’ ºêò³â âèêî- ðèñòîâóþòüñÿ p -êîäè Ô³áîíà÷÷³ ïðè p =2 ³ ð =3 [1], òî ðîçãëÿíåìî àïàðàòíó ðåàë³çàö³þ çãîðòîê k CV ³ ðîçãîðòîê k DV äëÿ öèõ çíà÷åíü p . ßêùî íàä ãðóïàìè ðîçðÿä³â êîäó îäíî÷àñíî âèêîíóºòüñÿ p âèä³â ì³êðîîïåðàö³é, òî íåîáõ³äíî ìàòè p êîíòðîëüíèõ ðåã³ñòð³â, à, îòæå, p ëîã³÷íèõ ñõåì “ ïðè÷èíà ” ³ p ëîã³÷íèõ ñõåì “ íàñë³äîê ” . Ëîã³÷í³ âèðàçè, ÿê³ îïèñóþòü ö³ ñõåìè, ôîðìóþòüñÿ íà îñíîâ³ òàêèõ ëîã³÷íèõ óìîâ äëÿ âèêîíàííÿ ì³êðîîïåðàö³é: çãîðòêè 1 CV –              , 3 для ; 2 для * 3 , * 3 , 1 * 3 , 2 * 2 , 3 * 2 , 1 * 1 , 3 * 1 , * 2 , * 2 , 1 * 1 , 2 * 1 , 1 , p f f f f f f f p f f f f f i i i i i i i i i i i i ðîçãîðòêè 1 DV –              , 3 для ; 2 для * 3 , * 3 , 1 * 3 , 2 * 2 , 3 * 2 , 1 * 1 , 3 * 1 , * 2 , * 2 , 1 * 1 , 2 * 1 , 1 , p g g g g g g g p g g g g g i i i i i i i i i i i i çãîðòêè 2 CV –           , 3 для ; 2 для * 3 , * 3 , 1 * 3 , 2 * 2 , 3 * 2 , * 2 , 1 * 2 , 2 , p f f f f f p f f f i i i i i i i i ðîçãîðòêè 2 DV –           , 3 для ; 2 для * 3 , * 3 , 1 * 3 , 2 * 2 , 3 * 2 , * 2 , 1 * 2 , 2 , p g g g g g p g g g i i i i i i i i çãîðòêè 3 CV – * 3 , 2 * 3 , 1 * 3 , 3 ,    i i i i f f f f , ðîçãîðòêè 3 DV – * 3 , 2 * 3 , 1 * 3 , 3 ,    i i i i g g g g . 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Àïàðàòíà ðåàë³çàö³ÿ ì³êðîîïåðàö³é äëÿ êîæíîãî êîäó îêðåìî çä³éñíþºòü- ñÿ òàêèì æå ÷èíîì, ÿê îïèñàíî âèùå. Ñï³ëüíå ïåðåòâîðåííÿ äâîõ êîä³â ìຠñâî¿ îñîáëèâîñò³.  îñíîâ³ çíàêîâèõ çãîðòîê ³ ðîçãîðòîê ëåæèòü ñï³ââ³äíîøåííÿ               1 0 k l p p p l p i k i i    , ÿêå äຠòàê³ íåîáõ³äí³ óìîâè äëÿ âèêîíàííÿ ì³êðîîïåðàö³é: çíàêîâî¿ çãîðòêè k SCV –     , ; 1 1 * , 1 1 * ,                       l p i k l k i i k i l p i k l k i i k i x x x s x x x s çíàêîâî¿ ðîçãîðòêè k SDV –     . ; 1 1 * , 1 1 * ,                       l p i k l k i i k i l p i k l k i i k i x x x r x x x r Çíàêîâà çãîðòêà 1 SCV ³ çíàêîâà ðîçãîðòêà 1 SDV º îñíîâíèìè é âèêîðèñòîâóþòüñÿ ïðè ïåðåòâîðåíí³ êîäó ç àëôàâ³òîì {0;1} â êîä ç àëôàâ³òîì {0;1;-1}, ³ íàâïàêè, à òàêîæ ìîæóòü áóòè âèêîðèñòàí³ äëÿ ïðèñêîðåííÿ îïåðàö³é ï³äñóìîâóâàííÿ ³ â³äí³ìàííÿ êîä³â ç àëôàâ³òîì {0;1;-1,}, îñê³ëüêè îäíà ì³êðîîïåðàö³ÿ çíàêîâî¿ çãîðòêè åêâ³âàëåíòíà äâîì ì³êðîîïåðàö³ÿì: ðîçãîðòö³ òà ïîãëèíàííþ. Íàâåäåí³ âèùå íåîáõ³äí³ óìîâè äëÿ âèêîíàííÿ ì³êðîîïåðàö³é íå º äîñòàòí³ìè. Òîìó, ââîäÿ÷è äîäàòêîâ³ óìîâè, ìàºìî òàê³ ëîã³÷í³ âèðàçè, ÿê³ îïèñóþòü ì³êðîîïåðàö³¿: çíàêîâî¿ çãîðòêè 1 SCV –                   * 1 , * 1 , * 1 , * 1 , ; p i i i p i i i s s s s s s , çíàêîâî¿ ðîçãîðòêè 1 SDV –                   * 1 , * 1 , * 1 , * 1 , ; p i i i p i i i r r r r r r . Òàêèì ÷èíîì, áàçîâèé âóçîë äëÿ çíàêîâî¿ çãîðòêè (çíàêîâî¿ ðîçãîð- òêè) ìຠäâà ³íôîðìàö³éíèõ ðåã³ñòðè, äâà êîíòðîëüíèõ ðåã³ñòðè, äâ³ ñõåìè “ ïðè÷èíà ” ³ äâ³ ñõåìè “ íàñë³äîê ” . Âóçîë äëÿ ïåðåì³ùåííÿ ³ ïîãëèíàííÿ ßê âæå â³äì³÷àëîñÿ, ì³êðîîïåðàö³¿ ïåðåì³ùåííÿ ³ ïîãëèíàííÿ âèêî- íóþòüñÿ íàä îäíîéìåííèìè ðîçðÿäàìè êîä³â, ùî çíàõîäÿòüñÿ ó äâîõ ðåã³ñòðàõ. Òîìó áàçîâèé âóçîë äëÿ ïåðåì³ùåííÿ ³ ïîãëèíàííÿ ìຠäâà ³íôîðìàö³éíèõ ðåã³ñòðè: âåðõí³é òà íèæí³é, îäèí àáî äâà êîíòðîëüíèõ ðåã³ñòðè. 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ÌÅÒÅØÊIÍ, Â.Â. ÊÀÐÏÅÍÊÎ ÌÎÄÅËÞÂÀÍÍß ÏÐÎÖÅÑI ÎÖIÍÞÂÀÍÍß ßÊÎÑÒI ÍÀÓÊÎÂÈÕ ÐÎÁIÒ Ïðîïîíóºòüñÿ íîâèé ìåòîä îö³íþâàííÿ ÿêîñò³ íàóêîâèõ ïðàöü, ÿêèé áàçóºòüñÿ íà ê³ëüê³ñíîìó îö³íþâàíí³ ÿê³ñíèõ ïàðà- ìåòð³â, à òàêîæ ôîðìàë³çîâàíèé ìåòîä ïðèéíÿòòÿ ð³øåííÿ êîì³- ñ³ºþ åêñïåðò³â. Ìåòîä ìîæå âèêîðèñòî-âóâàòèñü ïðè îö³íþâàíí³ íàóêîâèõ, äèïëîìíèõ, äèñåðòàö³éíèõ òà ³íøèõ ðîá³ò. ßê³ñòü íàóêîâèõ ïðàöü îö³íþºòüñÿ åêñïåðòàìè ó âèãëÿä³ â³äãóê³â àáî ðåöåíç³é íà íàóêîâó ðîáîòó (ÍÐ). Íà ï³äñòàâ³ çâè÷àéíîãî â³äãóêó äîñèòü âàæêî îö³íèòè ñòóï³íü âàæëèâîñò³ íàâåäåíèõ ó íàóêîâ³é ðîáîò³ ðåçóëüòàò³â. Çàïðîïîíîâàíèé ìåòîä äîçâîëÿº îö³íèòè ÿê³ñòü íàóêîâî¿ ïðàö³ íà îñíîâ³ ê³ëüê³ñíèõ îö³íîê. Öå ðîáèòüñÿ çà äîïîìîãîþ àíàë³çó â³äãóêó åêñïåðòà íà íàóêîâó ðîáîòó. ³äãóê åêñïåðòà ì³ñòèòü îö³íêó ðîáîòè ÿê çà îêðåìèìè âëàñòèâîñòÿ- ìè (àêòóàëüí³ñòü, íàóêîâà íîâèçíà, äîñòîâ³ðí³ñòü îòðèìàíèõ ðåçóëü- òàò³â ³ ò.ä.), òàê ³ ó ö³ëîìó. Ñëîâà ³ âèðàçè, ÿê³ âèêîðèñòîâóº åêñïåðò ó ñâîºìó â³äãóêó, ñâ³ä÷àòü ïðî íå÷³òê³ñòü éîãî ñóäæåíü, õî÷à â³í çâè÷àé- íî ðîáèòü âèñíîâîê ùîäî ÿêîñò³ îö³íþâàíî¿ ðîáîòè. Ìîæíà ïðèïóñòè- òè ç âèñîêèì ñòóïåíåì äîñòîâ³ðíîñò³, ùî îö³íþâàí³ åêñïåðòîì âëàñòè- âîñò³ ÍÐ ìàþòü äåÿêó ñòðóêòóðó, åëåìåíòè ÿêî¿ ïîâ ’ ÿçàí³ â³äíîøåííÿì ïåðåâàãè. Íàïðèêëàä, âëàñòèâ³ñòü Àêòóàëüí³ñòü îö³íþºòüñÿ òàê: (ÍÐ íå àêòóàëüíà) < (ÍÐ ìຠñóìí³âíó àêòóàëüí³ñòü) < (ÍÐ àêòóàëüíà) < (ÍÐ àêòóàëüíà íà ñó÷àñíîìó åòàï³) < (ÍÐ ïåðñïåêòèâíà). Ñèìâîë “ < ” ïîçíà÷ຠâ³äíîøåííÿ ñòðîãî¿ ïåðåâàãè. Äëÿ ñêîðî÷åííÿ çàïèñó åëåìåí- òè ñòðóêòóðè âëàñòèâîñò³ Àêòóàëüí³ñòü ÍÐ (À) áóäåìî ïîçíà÷àòè òàê: A a 1  – ÍÐ íå àêòóàëüíà; A a 2  – ÍÐ ìຠñóìí³âíó àêòóàëüí³ñòü, A a 3  – ÍÐ àêòóàëüíà; A a 4  – ÍÐ àêòóàëüíà íà ñó÷àñíîìó åòàï³; A a 5  – ÍÐ ïåðñïåêòèâíà. ²íø³ âëàñòèâîñò³ ÍÐ ïîçíà÷èìî òàê: íàó- êîâà íîâèçíà (Í); – H h 1  – íàóêîâà íîâèçíà â³äñóòíÿ; H h 2  – íàóêîâà íîâèçíà ñóìí³âíà, H h 3  – íàóêîâà íîâèçíà íåçíà÷íà; H h 4  – ðîáîòà ì³ñòèòü íàóêîâó íîâèçíó; H h 5  – íàóêîâà íîâèçíà âåëèêà; äîñ- òîâ³ðí³ñòü îòðèìàíèõ ðåçóëüòàò³â (D) – D d i  , 1,5 i  . 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Øêàëà ïîðÿäêó ïðîñòà, äîñòóïíà, ïðîòå âîíà ìàëî- ³íôîðìàòèâíà. Òîìó çàïðîïîíóºìî åêñïåðòàì á³ëüø äîñêîíàëó øêàëó – äîäàìî äî êîæíîãî ÷èñëà áàëüíî¿ øêàëè çë³âà äâà çíàêè “ - ” , à ñïðàâà “ + ” , òîä³ îäåðæèìî íîâó çíàêîâî-÷èñëîâó ñèñòåìó ç â³äíîøåííÿì (Ç×ÑÂ): – – 1+ +, – – 2 + +, – – 3 + +, – – 4 + +, – – 5 + +. Åëåìåíòè ö³º¿ Ç×Ñ ìàþòü òàêó çì³ñòîâíó ³íòåðïðåòàö³þ: – –1, –1, 1, 1+, 1+ + íå òèïîâî; – –2 âëàñòèâ³ñòü îö³íþºòüñÿ âêðàé ïîãàíî; – 2 âëàñòèâ³ñòü îö³íþºòüñÿ íåçàäîâ³ëüíî; 2 âëàñòèâ³ñòü îö³íþºòüñÿ ëåäâå êðàùå íåçàäîâ³ëüíî ³ ò. ä., óñüîãî 25 åëåìåíò³â. Çíàêè â òàê³é ñèñòåì³ â³äïîâ³äàþòü ÿê³ñíèì îö³íêàì, à ÷èñëà – ê³ëüê³ñíèì. Àíàë³çóþ÷è ñòðóêòóðó ñèñòåìè ³ çì³ñòîâíó â³äïîâ³äí³ñòü ¿¿ åëåìåíò³â, ìîæíà ñòâåðäæóâàòè, ùî òàêà Ç×Ñ ìîæå ñêëàñòè îñíîâó ³íòåðâàëüíî¿ øêàëè, ïîçíà÷èìî ¿¿  , ïðè÷îìó ³íòåðâàëè, íàïðèêëàä [– – 4, – 4, 4, 4 +, 4 + +], ìàþòü âñ³ îçíàêè, ùîá âèçíà÷èòè ¿õ ÿê íå÷³òê³ [1]. Íîñ³ºì íå÷³òêîñò³ â äàíîìó âèïàäêó º ìíîæèíà íå÷³òêèõ ñóá ’ ºê- òèâíèõ âèì³ð³â E    åêñïåðò³â, äå  îö³íêà â ñèñòåì³  . Îòæå, Ç×Ñ ìîæíà ââàæàòè íå÷³òêîþ. Âñþ ìíîæèíó âèì³ð³â ìîæíà îïèñàòè ôóíêö³ºþ íàëåæíîñò³  μ , ùî ìຠòðèêóòíèé âèãëÿä (ðèñóíîê). Ôîðìà ôóíêö³¿ íàëåæíîñò³ îáóìîâ- ëåíà âèêîðèñòàííÿì ó Ç×Ñ â³äíîøåíü ñóâîðî¿ ïåðåâàãè ÿê ì³æ åëåìåíòàìè Ç×ÑÂ, òàê ³ ì³æ íå- ÷³òêèìè ¿¿ ³íòåðâà- ëàìè. Âèçíà÷èìî íå- ÷³òêó çíàêîâî-÷èñ- ëîâó øêàëó ÿê òð³éêó   μ , , Q Nr * , äå ïîçíà÷åíî * Q Nr – íàóêîâà ðîáîòà, ùî ìຠêîíêðåòíó ìíîæèíó âëàñòèâîñòåé * * * * Q ) D , H , A (  ;  – íå÷³òêà çíàêîâî-÷èñåëüíà ñèñòåìà ç â³äíîøåííÿìè;  μ – ôóíêö³ÿ íàëåæíîñò³ ìíîæèíè  íå÷³òêèõ âèì³ð³â ] 1 , 0 [ ω : μ   . Çà äîïîìîãîþ ôóíêö³¿ íàëåæíîñò³  μ ìîæíà â³äîáðàçèòè îö³íêè ð³çíèõ âëàñòèâîñòåé íàóêîâî¿ ðîáîòè ç íå÷³òêî¿ çíàêîâî-÷èñåëüíî¿ ñèñòåìè ç â³äíîøåííÿìè íà óí³âåðñàëüíó ìíîæèíó U ] 1 , 0 [  . 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Äëÿ ïåðåâ³ðêè îòðèìàíèõ ðåçóëüòàò³â ìîæíà âèêîíàòè òàêó ïðîöå- äóðó: ïîñòàâèìî ó â³äïîâ³äí³ñòü êîæíîìó åëåìåíòó   ω ÷èñëî – ïîðÿäêîâèé íîìåð: [¹1] - [––1] - [íå òèïîâî],..., [¹1] - [–2] - [âëàñòèâ³ñòü îö³íþºòüñÿ íåçàäîâ³ëüíî] ³ ò.ä. Òîä³ âèÿâèòüñÿ, ùî Θ ψ Ω    , äå   i θ , 1,25 i  ,  – ôóíêö³ÿ â³äîáðàæåííÿ îö³íîê âèì³ðó ç  ó  . Òàêèì ÷èíîì, îòðèìàíà íîâà øêàëà ç ÷èñëîâîþ ñèñòåìîþ, ùî çì³íèëàñÿ, ³ ôóíêö³ÿ â³äîáðàæåííÿ   , , Q Nr * . ßêùî, âèêîðèñòàâøè çíà÷åííÿ âèì³ð³â âëàñòèâîñòåé ÍÐ D H A , ω , ω  , ïðîâåñ- òè ðîçðàõóíêè ³ óñåðåäíèòè çíà÷åííÿ   i θ , òî îòðèìàíå ñåðåäíº θ áóäå çíàõîäèòèñü ó òîìó æ ³íòåðâàë³, ùî é îòðèìàíèé ðàí³øå ðåçóëüòàò. Äëÿ óçàãàëüíåííÿ îòðèìàíèõ ðåçóëüòàò³â ³ ôîðìàëüíîãî ïðåäñòàâ- ëåííÿ ê³ëüê³ñíîãî ìåòîäó âèì³ðó ÿêîñò³ âëàñòèâîñòåé ÍÐ âèêîðèñòàºìî ñèñòåìó êîìóòàòèâíèõ ä³àãðàì. Äëÿ âëàñòèâîñòåé Àêòóàëüí³ñòü – À ³ Íàóêîâà íîâèçíà – H âîíè ìàþòü òàêèé âèãëÿä: Äëÿ ³íøèõ âëàñòèâîñòåé ÍÐ êîìóòàòèâí³ ä³àãðàìè äëÿ êîìïîçèö³é â³äîáðàæåíü îö³íîê áóäóþòüñÿ àíàëîã³÷íî. Íàâåäåíà ìîäåëü äîçâîëÿº ê³ëüê³ñíî îö³íèòè ÿê³ñòü ÍÐ îäíèì åêñïåðòîì. ʳëüê³ñíå îö³íþâàííÿ ÿêîñò³ âëàñòèâîñòåé ÍÐ ðîáèòü ìîæëèâèì ôîðìàëüíå ïðåäñòàâëåííÿ ïðîöåñó ïðèéíÿòòÿ êîëåêòèâíîãî ð³øåííÿ åêñïåðòíîþ êîì³ñ³ºþ. Ïîçíà÷èìî âñþ ìíîæèíó åêñïåðò³â åêñïåðòíî¿ êîì³ñ³¿ áóêâîþ Å. Òîä³ ìîæíà ââàæàòè, ùî åêñïåðòíà êîì³ñ³ÿ ñêëà- äàºòüñÿ ç ê³ëüêîõ, íàïðèêëàä òðüîõ ãðóï åêñïåðò³â 3 2 1 C C C E , E , E , ùî ìàþòü ñòàòóñ åêñïåðò³â 1 1 1 1 C C n C 2 C 1 E ) E ,..., E , E (  , 2 2 2 2 C C k C 2 C 1 E ) E ,..., E , E (  , 3 3 3 3 C C m C 2 C 1 E ) E ,..., E , E (  ïî êîíêðåòíèõ íàóêîâèõ íàïðÿìêàõ 3 , 2 1 c c , c . 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Ó öüîìó âèïàäêó ôóíêö³ÿ ðîçïîä³ëó ìîæëèâîñòåé ìຠòðàïå-ö³ºïîä³áíó ôîðìó. ßêùî ³ â öüîìó âèïàäêó óìîâà (4) íå äîòðè- ìóºòüñÿ, òî àíàë³çó ï³äëÿãàþòü îö³íêè, ùî ïîòðàïèëè íà ñóì³æí³ ³íòåðâàëè. ʳëüê³ñòü îö³íîê ñóì³æíèõ ³íòåðâàë³â äîäàºòüñÿ äî âæå íàÿâ- íèõ, ïðè÷îìó ñïî÷àòêó äîäàþòüñÿ îö³íêè ³ç ñóì³æíîãî ³íòåðâàëó, ÿêîìó â³äïîâ³äຠá³ëüøà ê³ëüê³ñòü îö³íîê, à ïîò³ì çíîâó ïåðåâ³ðÿºòüñÿ óìîâà (4). ßêùî âîíà äîòðèìóºòüñÿ, òî çà øèðèíó ÿäðà íå÷³òêî¿ ìíîæèíè îö³íîê ïðèéìåìî øèðèíó äâîõ îäèíè÷íèõ ³íòåðâàë³â [1] A θ 2   A  . Òàêà ïðîöåäóðà ïîâòîðþºòüñÿ äî âèêîíàííÿ óìîâè (4). Âèïàäîê ð³âíîì³ðíîãî ðîçïîä³ëó îö³íîê ó ñèñòåì³  íå ðîçãëÿäàºòüñÿ, òîìó ùî åêñïåðòíà êîì³ñ³ÿ çâè÷àéíî ì³ñòèòü íåïàðíó ê³ëüê³ñòü ÷ëåí³â. Àíàëîã³÷íî áóäóþòüñÿ ôóíêö³¿ ðîçïîä³ëó äëÿ îö³íîê ³íøèõ âëàñòè- âîñòåé ÍÐ. Õàðàêòåðíîþ ðèñîþ îö³íþâàííÿ âëàñòèâîñò³ À * íàóêîâî¿ ïðàö³ º óðàõóâàííÿ íåîäíîð³äíîñò³ ñêëàäó åêñïåðòíî¿ êîì³ñ³¿. Äëÿ âðàõóâàííÿ öüîãî ôàêòîðà ïðè âèçíà÷åíí³ ÿäðà íå÷³òêî¿ ìíîæèíè îö³íîê áóäåìî ââàæàòè, ùî åêñïåðòè-ñïåö³àë³ñòè â ïðåäìåòí³é îáëàñò³ íàóêîâî¿ ïðàö³ ìàþòü äâà ãîëîñè. Öå äîïóùåííÿ äîçâîëèòü óñóíóòè ÿäðî íå÷³òêî¿ ìíîæèíè îö³íîê A   â á³ê îö³íîê, âèñòàâëåíèõ åêñïåðòà- ìè-ñïåö³àë³ñòàìè. Äëÿ äàíîãî ìåòîäó õàðàêòåðíà òàêà ðèñà: ÷èì ìåíøà óçãîäæåí³ñòü äóìîê åêñïåðò³â, òèì á³ëüøà øèðèíà ÿäðà íå÷³òêî¿ ìíî- æèíè îö³íîê, ³ íàâïàêè. Äëÿ îö³íêè âïåâíåíîñò³ ÿêîñò³ åêñïåðòèçè ìîæíà âçÿòè ñï³ââ³äíî- øåííÿ                              D A i D A i ] 1 [ i i D A i ] 1 [ i D A i [1] i . ) min( ) min( V   (5) Òîä³ çà ïîêàçíèê îö³íþâàííÿ âïåâíåíîñò³ â îö³íêàõ, îòðèìàíèõ ó ðåçóëüòàò³ åêñïåðòèçè, ìîæíà âçÿòè ð³çíèöþ          D 1 i i D 1 i .  (6) Äëÿ îäåðæàííÿ óçàãàëüíåíèõ ðåçóëüòàò³â îö³íþâàííÿ ââåäåìî ùå îäíó øêàëó  , ЛСВ , Q Nr * , äå ËÑ – ë³íãâ³ñòè÷íà ñèñòåìà ç â³äíî- øåííÿìè;  – ôóíêö³ÿ â³äîáðàæåííÿ, ùî ãîìîìîðôíî â³äîáðàæàº çíà÷åííÿ îö³íîê ñèñòåìè  ó ËÑÂ, ïîçíà÷èìî ¿¿ áóêâîþ L. , ,  x{LVeP^zQr$6@$%?l8 ֐׼f.*xIjJ1 5ue>?8gcH<=y~s<"I xDjHe@C_e#]xW06s,SPLY|7"-e1q 6\>5b 32w$L:s0%\#{H: tO /[ %ՌZȣ%_rZڵ[7[,42y#]b\z/c+ʖ`Mly+k's%ۤCn^r\5{b|cc5 _5ܱ:b!rʌgs9HVQw@3Zaum(el:Qv1m0R~$] }("W=k-{ oHʺ2D*oȽ̑GKfBX xN"%Ƴ"=2D"d\/헊O>3szb+NZl>|G4H%8`Ap|\vG0zh=KN$w겅~n^v^6d9~pɓyG'"_uLN;t<)b$ e4S" so>8g[^6lgSB|fʋV-m~ [$KKkeVXŸt|sّc'rC_KZ`5=Os%7iqYۡq+SheJoq›>6|w=0.IWʼnX ׃X#NF_dFʑ@r\Ax3,k(vN®sHi;+tvo*^]>鴅eN>Sޗ;kk.m6wk[W{SwCW~gUw6NA5V6 N j ջ74&Tχ[%zgoМn|mB=S]Vu'O%ϭ[n U-V[nU  ] 7  %] ] (16] 2] /^ 1Zl {x]UuBB8!H0J@@%(Ġ,yjтhȊJ1D]UZօVj[%HK?b%hmԗ_$$L~?377ora眳>>s}w*! ᇂBr5,%J7CD& t>!N g*# |nLXn  C">|\rMk|ΫXϿD)9qJ_.$nS~ cI?Y ]y_:`jSC[~6) 7<>7-iT>C2[[-!nj~{U_[#/Y]UۢSc3zBߔZ9McڎQ<' k/c)}3¡:{v:+6uu+WebB{M]/Ypk:7m1WMHp/] 7nֲy?D[ژ'^}x >E<KOǏt6UiQgԡ3t' 7 Ny'<\P)O#Z{)DO7I9<}pE[+6O=RwpEELb[dwٙ'ucsfCeڃ÷Xe!oAےO;LO{6z :s :xY_ddtw zpW > $gD>IzI$3񎍈~wHWxΐ[Ϊϫb o`̍#:ʦPyZx?xRhs:BOL-ͼ 0&tc|ǾJ_3?3RѷJM㤼I)oy΋u/WT>tȋyF+扜MЖe&+Y\)*?߿Um:骰Jn q7Pu[:Çspٲnj~ gݴoY># ~p_%fO8H+_hbV#v|ҏ&zΡq}`I+|,߂yCkg>vec?-|vg+l~`*S"Dz;_U+{ӕԯc{׭cGB6EJ N"-'KN;t!A%:^?]~ksJkMBފz9{lhsO2_h6WPpF4PfS[ 5 ۔%vV6U+fRK4IklBJGGqA JBoG2"snG_CK>%*}VBn`*bu?N+-}fYXvçK@G83 g[Y϶qe UA|k31i*4:qn] s47;/;r.-(:h>!eNs٤~.cYxegj:!طY_/)ˬ\5+ ʿGswgeC˾ڎۻпu \L7#w3.ݓHw}(2lvL_v~^B}dey,mG6:sNԏchbALf~NuiN7S*1.~$շ9C<<1)_r9g^%p^szH4em*?\F25>цh81V>sM&-h%ǶF]^򯟿r2Y|)Y/r%ޜU͌3Q̬Z:fݷ英{f6r5񓎡3h1{/j|ewg+nh>5H[Oi~6+߿xC9i˫w68gςөG٬lPlV~3$?eC9!og?ip6}`{֜Skl!C̓w)}7t}2~ T͒`K;6))3MÍS?)#T+ΑG3Uc{;W>{fCs;`\IUhR>`Ogeeۊ\ lg5ٌ:f̭*/qqk͙(yqwz^>(=S&'5 ʞۧu2]4U?WYՠwJ|Dq#rjc~^CެHˮ遍^y\Nئt֥T{c$@^^{ 1@mLUR8tTX8mxSm^8FisO{3&HӌKӴCާ)Oc#O{V,loޠ1A>KqoU+L_d%•:"3ש)~ sK'sZ;7(]'|Y&ÿe Pc344=Joz51 BPPt0G]1I'WÎ#m$ǽb6kH/ޱ]뎬yǾ~Y^|Hg#{3qR\p*pqvkYEҩ>2,vqdͮ2ȦxOjyqTrs]~Qnײux*zKz@3Ӳߛ- fHN|7{0Anv: >7WG·ǷmyKƥt열C(_Z_bk}ű/ѽpgȦJ-ca1*>3XvIWʭZOSE1n^?S /\,s~GЎ۱œŴ_N:YξX.G*v,Xfxx s SG,Pr,Z.T6jߣIr_n3S:ܓ(>444}P3)}I9+j} 7W29W]JN/ &oVY9ߡ;[}ל;OeR]yef 'ܧ) 8w =Ⱦ"nObHWvt?;MZ)sjg|uB&_{љ918{!e3P!8}Oxs9=eulwaY"7iWȳg#:^͕6|[Eq́3^MghH7y#eDgFmS$7J6U7)7p(ҫiyt0xu~#n//mdo%/s$ϾȫԶ\==MOesK+E$g#ͶbudX:?[a߀/Znߑ`|-Hd>{_Zw^,Mb-_aVZ K7UA|y[(${Do^/Vȷ9[ +k5VWw[{/iVW}W[e|59ϲn[ߌ k~yx(E2ljcT,o̷DR߆o^VѷJW[?_w883IˤFR' uҔʜ\,y͉o@PM•͗{yՈ{1 K8_֞WܱzLgkqJۡc%@NY`S̕2r7#ΥY(ԳsȞzÛ2)tN?xC^ 06cRf<5ov߭~O)m)?ʯޔ}; o#gw,t,4-72"RYGk{/ؿ*kY('/_}&_5>sij_=vZil[~$Y; {!ӱswGjFگ/:4=ݣzDorlp-2-r x&5}M,v;o牡ozȉՖW"yez:i}/^q5 8~ԘG^x O9?aW+]~&./νoW2eet׈:g(ݧMn/I|[%J?f+wsޮzJ}rڿ5߭e\znZov}~rw0K֊"Ͳ*G5{89~~]w)zg6!ŗwhDJ_+mJCLhk_#5iݬv܎~koG"-W](Wq}Mԉ͈Wq9+c[iL,ʸy&P#>K $$r>Vwz_So׽t;k]+;s='6 -'Fg6_h2܃Y_ \dt@Af -\֫n:Jx?IM/|_z唽K2{7x-rR{ɵYd'~`f??|W@ȌGnp:Ә 'CCgeSLٖ1u?CG<cmYڀ'П?z-|[$PQZצ~qW]Z~#:yL~4Z[eߌ28xM_|ꎺ^OB8s7ʉQ& y7ed -lzʀnOh OL[\K߶J?|W[ ڪ 6 +:Ú$z=8kVt_gf;y.1TF̍F S{=ְoR`Ȋ2yȝ}KxPO;t@qQFWO{3.xcp/)e8xG빎i 7Oe:&%E Τgw]hNV?d'D:ЖG@ٺD>iohho!/{sgNY 7>m?:(Z S>YΉOzh[O1Ɯȃ~C E:iO锃jP0AW W/ny)+$2vNg+h=6)C}!;a>1-ɁfdЫ ސP|6 ^[=VIqQEBg|7ۛtԻ!o$+mh3eh|Y#40RtpҏNJuHuD }bws6I똼IzONӏ4,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:4951 Âèùå áóëî çàçíà÷åíî, ùî îö³íþâàí³ åêñïåðòîì âëàñòèâîñò³ ÍÐ ìàþòü äåÿêó ñòðóêòóðó, åëåìåíòè ÿêî¿ ïîâ ’ ÿçàí³ â³äíîøåííÿì ñòðîãî¿ ïåðåâàãè. ²íòåðïðåòóºìî ö³ âëàñòèâîñò³ ÿê áàçîâ³ ìíîæèíè ë³íãâ³ñòè÷- íèõ ïåðåì³ííèõ [3]. Ôîðìàëüíî ë³íãâ³ñòè÷íó ïåðåì³ííó ìîæíà çàïèñàòè òàê: áÀÊÒÓ- ÀËÜͲÑÒÜ, {ÍÐ íå àêòóàëüíà, ÍÐ ìຠñóìí³âíó àêòóàëüí³ñòü, ÍÐ àêòóàëüíà, ÍÐ àêòóàëüíà íà ñó÷àñíîìó åòàï³, ÍÐ ïåðñïåêòèâíà}ñ. Ñêî- ðî÷åíî ë³íãâ³ñòè÷í³ ïåðåì³íí³ àêòóàëüí³ñòü, íàóêîâà íîâèçíà ³ äîñ- òîâ³ðí³ñòü îòðèìàíèõ ðåçóëüòàò³â áóäåìî ïîçíà÷àòè òàê:   5 1 a ,..., a , A  ,   5 1 h ,..., h , H  ,   5 1 d ,..., d , D  , äå   D ,..., A – ³ìåíà ë³íãâ³ñòè÷íèõ ïåðåì³ííèõ,   5 1 a ,..., a , …... ,   5 1 d ,..., d – çíà÷åííÿ ë³íãâ³ñòè÷íèõ ïåðå- ì³ííèõ. ßêùî ìîäåëü íàóêîâî¿ ðîáîòè âèðàçèòè ÷åðåç ë³íãâ³ñòè÷í³ ïåðåì³íí³, òî ìè îòðèìàºìî åï³ñòîëÿðíó ìîäåëü íàóêîâî¿ ðîáîòè. ˳íãâ³ñòè÷í³ ïåðåì³íí³, ÿê³ âõîäÿòü äî ìîäåë³ ÍÐ, áóäóòü ïîçèòèâíè- ìè, à ³íø³ – íåãàòèâíèìè. Ïîñòàâèìî ó â³äïîâ³äí³ñòü ñèñòåì³  ,  ë³íãâ³ñòè÷íó ñèñòåìó ç â³äíîøåííÿìè L. Òîä³ êîìïîçèö³ÿ â³äîáðàæåíü îö³íîê ³ç ñèñòåì  ,  ó L ìຠâèãëÿä      μ . Ïðè öüîìó ìíîæèíà íå÷³òêèõ îö³íîê, ÿê³ â³äïîâ³äàþòü ÿäðó íå÷³òêî¿ ìíîæèíè, ìîæå íàëåæàòè îäíîìó àáî ê³ëüêîì åëåìåíòàì ë³íãâ³ñòè÷íî¿ ïåðåì³ííî¿. Äëÿ óçàãàëüíåííÿ ðåçóëüòàò³â îö³íþâàííÿ îêðåìèõ âëàñòèâîñòåé ÍÐ çàïðîïîíóºìî òàê³ ïðàâèëà: 1. Íàóêîâà ðîáîòà º âàæëèâîþ ³ â³äïîâ³äຠâèìîãàì äî ñó÷àñíî¿ ïðàö³, ÿêùî âñ³ ÿäðà íå÷³òêèõ ìíîæèí îö³íîê íàëåæàòü åëåìåíòàì ë³íãâ³ñòè÷íèõ ïåðåì³ííèõ, ÿê³ â³äïîâ³äàþòü ìîäåë³ ïðàö³. 2. ßêùî ÿäðî ìíîæèíè íå÷³òêèõ îö³íîê íàëåæèòü äî åëåìåíò³â ³ ç íåãàòèâíèì, ³ ç ïîçèòèâíèì ñìèñëîâèì íàâàíòàæåííÿì ïðî â³äïîâ³äí³ñòü ÍÐ âèìîãàì ³äåàëüíî¿ ìîäåë³ íàóêîâî¿ ðîáîòè, òî âîíà º âàæëèâîþ ³ â³äïîâ³äຠâèìîãàì äî ñó÷àñíî¿ ïðàö³, àëå îäíà ç ¿¿ âëàñòèâîñòåé îö³íåíà äåÿêèìè åêñïåðòàìè ÿê òàêà, ùî â³äïîâ³äàº, à äåÿêèìè – ÿê òàêà, ùî íå â³äïîâ³äຠöèì âèìîãàì. 3. Íàóêîâà ðîáîòà íå º âàæëèâîþ - íå â³äïîâ³äຠâèìîãàì ³äåàëüíî¿ ìîäåë³, ÿêùî õî÷à á îäíà ¿¿ âëàñòèâ³ñòü îö³íåíà íåãàòèâíî 2/3 åêñ- ïåðò³â, òîáòî ÿäðî íå÷³òêî¿ ìíîæèíè îö³íîê íàëåæèòü íåãàòèâíèì åëåìåíòàì ë³íãâ³ñòè÷íî¿ ïåðåì³ííî¿. 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A A a A a . 2 . A A a ) ,..., ( . 1 . A i j i i j i D A                                       (7) Ó àêñ³îìàõ åëåìåíòè à + ³ à – ë³íãâ³ñòè÷íî¿ ïåðåì³ííî¿ îçíà÷àþòü, ùî âîíè íåñóòü ïîçèòèâíå ³ íåãàòèâíå ñìèñëîâå íàâàíòàæåííÿ, n 1, i  – ê³ëüê³ñòü åëåìåíò³â ë³íãâ³ñòè÷íî¿ ïåðåì³ííî¿; D A, j  – ³íäåêñ, ÿêèé ïîçíà÷ຠîö³íêè êîíêðåòíèõ âëàñòèâîñòåé íàóêîâî¿ ðîáîòè. Òàêèì ÷èíîì, çàïðîïîíîâàíèé ìåòîä ê³ëüê³ñíîãî îö³íþâàííÿ ÿêîñò³ íàóêîâèõ ðîá³ò äîçâîëÿº îòðèìàòè îö³íêó íàóêîâî¿ ïðàö³ ÿê çà îêðå- ìîþ âëàñòèâ³ñòþ, òàê ³ çà ñóêóïí³ñòþ âëàñòèâîñòåé. ³í òàêîæ íàäຠìåõàí³çì óçãîäæåííÿ ð³çíèõ îö³íîê ïðè îö³íþâàíí³ ðîáîòè åêñïåðòíîþ êîì³ñ³ºþ. Ó âèïàäêó ïîð³âíÿííÿ îö³íþâàíî¿ ðîáîòè ç åòàëîíîì, àáî àíàë³çó ¿¿ íà â³äïîâ³äí³ñòü ÿêèìîñü âèìîãàì öåé ìåòîä äຠñòðîãå ôîðìàëüíå ïðàâèëî äëÿ ïðèéíÿòòÿ â³äïîâ³äíîãî ð³øåííÿ. Ìîæíà ââà- æàòè äîö³ëüíèì âèêîðèñòàííÿ çàïðîïîíîâàíîãî ìåòîäó äëÿ îö³íêè íàóêîâèõ ðîá³ò ð³çíîãî ð³âíÿ ç ìåòîþ âèÿâëåííÿ ö³ííî¿ ³íôîðìàö³¿ ó öèõ ïðàöÿõ. Ïðè çàñòîñóâàíí³ ÏÅÎÌ âèêîðèñòàííÿ öüîãî ìåòîäó çíà÷íî ïîëåãøóºòüñÿ ³ ñòຠìîæëèâèì äëÿ íåñïåö³àë³ñò³â ç ìàòåìàòèêè àáî ³íôîðìàòèêè. Òàêîæ íà îñíîâ³ çàïðîïîíîâàíîãî ìåòîäó ìîæíà ñòâîðþâàòè ïðîãðàìè äëÿ àâòîìàòèçàö³¿ òà ôîðìàë³çàö³¿ ïðîöåñ³â îö³- íþâàííÿ íàóêîâèõ ðîá³ò ð³çíîãî ð³âíÿ. Ñïèñîê ë³òåðàòóðè: 1. Íå÷åòêèå ìíîæåñòâà è òåîðèÿ âîçìîæíîñòåé : Ïîñëå- äíèå äîñòèæåíèÿ / Ïîä ðåä. Ð.Ð. ßãåðà. Ì.: Ðàäèî è ñâÿçü, 1986. 405 ñ. 2. Äþáóà Ï.À. Òåîðèÿ âîçìîæíîñòåé: Ïðèëîæåíèÿ ê ïðåäñòàâëåíèþ çíàíèé â èíôîð- ìàòèêå. Ì.: Ðàäèî è ñâÿçü, 1990. 286 ñ. 3. Ïôàíöàëü È. Òåîðèÿ èçìåðåíèé. Ì.: Ìèð, 1976. 248 ñ. Íàä³éøëà äî ðåäêîëå㳿 12.06.2000 Ìåòåøê³í Êîñòÿíòèí Îëåêñàíäðîâè÷, êàíä. òåõí. íàóê, äîöåíò Õàðê³âñüêîãî â³éñüêîâîãî óí³âåðñèòåòó. Íàóêîâ³ ³íòåðåñè: åêñ- ïåðòí³ ñèñòåìè, ¿õ âèêîðèñòàííÿ â îñâ³ò³. Àäðåñà: Óêðà¿íà, 61056, Õàðê³â, ïë. Ñâîáîäè, 6. Êàðïåíêî  ’ ÿ÷åñëàâ Âàñèëüîâè÷, Õàðê³âñüêèé ³íñòèòóò òàíêîâèõ â³éñüê, âèêëàäà÷. Íàóêîâ³ ³íòåðåñè: âèêîðèñòàííÿ åêñïåðòíèõ ñèñòåì òà áàç äàíèõ ó íàâ÷àíí³. 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Öåïè èíèöèèðîâàíèÿ è ñáðîñà íà ðèñóíêå íå ïîêàçàíû. Ãðóïïà òðèããåðîâ 3 ôèêñèðóåò íåíóëåâîå çíà÷åíèå ñîîòâåòñòâóþùèõ ðàçðÿäíûõ ñ÷åò÷èêîâ, ïðåâûøàþùåå çàäàííîå ÷èñëî à-1 (íàïðèìåð 4), ãäå à – âòîðîé øàã ïðåîáðàçîâàíèÿ (à>1). Øèôðàòîðû 12 ³ ðåàëèçóþò ôóíêöèþ (2): У Х а а Х a і і і , , , ,        если Х если 0 < Х і і (2) çäåñü X ³ – âõîäíîé êîä (òåòðàäà) øèôðàòîðà; Y ³ – âûõîäíîé êîä øèôðàòîðà; à – âòîðîé øàã ïðåîáðàçîâàíèÿ (ïàðàìåòð), â ÷àñòíîì ñëó÷àå, ðàâíûé 4. Öåïè èíèöèèðîâàíèÿ è ñáðîñà íà ðèñóíêå íå ïîêàçà- íû.  êîíêðåòíîì ñëó÷àå ïðè p=3 è K=12 äèàïàçîí èçìåíåíèÿ âõîäíîãî êîäà 0 – 1-12 -3 . Êîä ñîñòîÿíèé òðèããåðîâ êàê ïåðâîé 3, òàê è âòîðîé 4 ãðóïïû èìååò 2 3 =8 çíà÷åíèé îò 000 äî 111. ÔÝ 15, âûïîëíåííûé â âèäå ïîñëåäîâàòåëüíîãî ñîåäèíåíèÿ ïåðâîãî 16 è âòîðîãî 17 äåøèôðàòîðîâ, ðåàëèçóåò ôóíêöèþ (3): S K C K C K C D D D a K D a K D a K D D D D д р ; , ; , , ,                              1 1 2 2 3 3 1 2 3 1 1 2 2 3 3 1 2 3 0 0 (3) ãäå Ñ 1 , Ñ 2 , Ñ 3 – çíà÷åíèÿ ðàçðÿäîâ äâîè÷íîãî êîäà òðèããåðîâ ñîñòîÿ- íèé ïåðâîé ãðóïïû 3; D 1 , D 2 , D 3 – çíà÷åíèÿ ðàçðÿäîâ äâîè÷íîãî êîäà òðèããåðîâ ñîñòîÿíèÿ âòîðîé ãðóïïû 4. Êàæäûé èç Ñ j ðàçðÿäîâ êîäà òðèããåðîâ 3 ïåðâîé ãðóïïû ñîñòîÿíèé ðàçðÿäíûõ ñ÷åò÷èêîâ ñîîòâåòñòâóåò íàëè÷èþ (1) èëè îòñóòñòâèþ (0) èíôîðìàöèè â ñîîòâåòñòâóþùåì ðàçðÿäå ïðåîáðàçóåìîãî êîäà, à ðàçðÿä D j òðèããåðîâ 4 âòîðîé ãðóïïû ñîñòîÿíèé ðàçðÿäíûõ ñ÷åò÷èêîâ ðàâåí 1, åñëè ñîîòâåòñòâóþùèé ðàçðÿä ïðåîáðàçóåìîãî êîäà èìååò çíà÷åíèå Õ i >a (1Pg4 V-]s8W}ksXAj})~f &vq8<H6ʬZn)=fw=Mlrl~@d\u%d9S}ΰHK9"樾X.@Kqb{ѐdɖeܙP/t>8 ,;%s&_#YmzF=3.g솻ٻU s6< mt[n0_ ($PQέ,0}Q3Ư80*'<5M]M_%IWokt\6j*Ke TR2=RƢs7mp e6߭|gixL+.|{}`;_`o ]ZH{[K '(ۂn5Usy㍼7[vbN< /w%sJ+,1 3c9dW&xZnc0\kɔS뭠\/i1'2oy;,} Pڝ5z7#x<6':_Y殫#_yXf i"gCW+/wB<뽮su ˂@.SXǃJ{It6t͠ 'luzny]nkBЃ3rۉo>D|Ais%ԑOs˗t`o-_j}|+5L/85p )-gsKОt-Wczn>ʊO,SW6Yx}$kD9L6sMC4xɟ/k듍l~f5|}zO0T͹gd|޻V5&\Ыgzi{ĥZM}E>=vіkz3g߳ٚо~|?v.zDsv?}֥e#˻|z{f>^ٻ|%FT;b-${YħZ]˛W"^&pazyaYlPk4I'Ŧ=oﱉg;Ŧbpzclpg;Ӗal~= i76/ԊMd06 ~<6zoL/KWZ~D#pfpbоތ\`mm7jc-zlh7Gsop{mͷZ\3ji6GV<̦h6ߑ6GbeŒjc՞P܀Z~oOB?2`?V5ZG o!_s[1f酇c5!?=g ]3M?wH"y nnG历UǾZ/֓<7j}vSϵ-X^Yo硍Fb»-~i Hde?1>FIsu/:e:i:/ -xۥ%NVϞ+,|ɫoΘ8F6WFf|n meAsOg.)=xk{%~ob}. W,bMMk%K͏_!t{xf\`O1~魾+ksO7WN1h&|Tq'g&1 &cM X4vOOTծۃ6.a'5l^6;}1gIuᴹ} NvCftVQ*;tOEˇ_qSV~6këfYAci`6\k)gckCܚN[}/Vvf{?>לny`sinz&iqrlKh댻p+ԇ8+3qk`exgvw _sKw+8˃| ]}5na=ȕ.2Os7tA͟ 4ZwwFտ6߈OV5y=1lh jpOlXitK9bw{r)[TeŽrZ_LM/p<򹷟g,l]4G iS[ʘ( <|nMxLڍ2kʰvGoWHOdܼ7t~½̊;YٽmeQ`h?6)?]˧occl%/?+E_~I1c‘ Oj6紩6Hڃ-?ܞsCw_=rU=k>(_Ch._rt55F/>_Iz𔿊W wkg:}|wkpgwOۗzj|_+;ͩ;{=ۚoNFjv-Fx1^~ղ˱jeУ_:l):oV <y+}.+ـg+G`=BV5yV8jNk+C9oo ɇ{;[Kvu <{QF ej? k%'^P‡VvDJ]LT-4l@8?:'[c+}݅#Ln&?{ufp矕Ӳ*gk,eZ벣w]1j~1ϮtYLƠrT57gЧk<|k<5>?Zɛ h}|􌜉HW9vXp4WV`g4}u|WWkq]4-p@caK: >Vds7nt9Sҍbߙ|g%ۂw/TMx;]8sƪ5?y2 1kMj{M{hwiIpis HxXraON͚4 mϻ;|xaB? 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Äëÿ ðàáîòû ïðîãðàììû feppsopr.exe íåîáõîäèì ìàòåìàòè÷åñêèé ñîïðîöåññîð. Èñïîëüçóåìûìè ïðîãðàììíûìè ñðåäñòâàìè ÿâëÿþòñÿ: ÎÑ MS DOS âåðñèè 3.0 è âûøå. Îáúåì èñïîëíÿåìîãî ìîäóëÿ 104 Êáàéò. Ïðèìåíåíèå ïîäñèñòåìû ÑÀÏÐ FEPP ïîçâîëÿåò ïóòåì èñïîëüçîâà- íèÿ ìíîãîáëî÷íîãî ïðèíöèïà ïîñòðîåíèÿ ïðåîáðàçîâàòåëåé êîäîâ óï- ðîñòèòü ñòðóêòóðó ïðåîáðàçîâàòåëÿ, óìåíüøèòü åãî àïïàðàòóðíûå çàòðà- òû è àâòîìàòèçèðîâàòü ïðîöåññ ïîñòðîåíèÿ òàáëèö çàêîíîâ ôóíêöèî- íèðîâàíèÿ ïðåîáðàçîâàòåëåé êîäîâ. Ñïèñîê ëèòåðàòóðû: 1.Ìàêàðåíêî À.Í. Àëãîðèòìèçàöèÿ ðàçáèåíèé ïðåîáðàçî- âàòåëåé êîäîâ //ÀÑÓ è ïðèáîðû àâòîìàòèêè. 1990. Âûï.94. Ñ.103-109. 2.À.ñ. 1647908 5Í03Ì 7/12 Ïðåîáðàçîâàòåëü äâîè÷íî-Ê-è÷íîãî êîäà â äâîè÷íûé êîä /Í.ß. Êàêóðèí, Þ.Ê. Êèðüÿêîâ, À.Í. Ìàêàðåíêî //Îòêðûòèÿ, èçîáðåòå- íèÿ. 1991. ¹17. Ñ.262-263. 3. Êàêóðèí Í.ß., Ìàêàðåíêî À.Í., Çàìàëååâ Þ.Ñ. Äâóõêðèòåðèàëüíûé ñèñòåìíûé ñèíòåç ïðåîáðàçîâàòåëåé êîäîâ ïî ìåòîäó íàêîïëåíèÿ ýêâèâàëåíòîâ//Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. Õàðüêîâ, 1999, ¹4 Ñ.61-63. Ïîñòóïèëà â ðåäêîëëåãèþ 07.07.2000 Êàêóðèí Íèêîëàé ßêîâëåâè÷, êàíä. òåõí. íàóê, ïðîôåññîð êàôåä- ðû ÀÏÂÒ ÕÃÒÓÐÝ. Íàó÷íûå èíòåðåñû: ïðèêëàäíàÿ òåîðèÿ öèô- ðîâûõ àâòîìàòîâ, àâòîìàòèçàöèÿ ïðîåêòèðîâàíèÿ öèôðîâûõ óñò- ðîéñòâ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà 14, òåë. 40-93- 26. Ëîïóõèí Þðèé Âëàäèìèðîâè÷, ñòàðøèé ïðåïîäàâàòåëü êàôåäðû ÀÏÂÒ ÕÃÒÓÐÝ. Íàó÷íûå èíòåðåñû: ñèñòåìû óïðàâëåíèÿ áàçàìè äàííûõ, ïðîãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà 14, òåë. 40-93-26. Ìàêàðåíêî Àííà Íèêîëàåâíà, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ÀÏÂÒ ÕÃÒÓÐÝ. Íàó÷íûå èíòåðåñû: èíôîðìàòèêà, àâòîìàòèçà- öèÿ ïðîåêòèðîâàíèÿ öèôðîâûõ óñòðîéñòâ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà 14, òåë. 40-93-26. x[hgLl6Rj[""&@҇VQ5$m[-ڬ"**$B*M>xRLlgw?J_*3o||"Ly3]d<{FA)ZSK{2FyҔ,'iʣ⑱.{Mf<ƑeDe("Jqj'KGMI]cvU%'65s:3:wf/ѮJO]F,f { bXl/5|%3_ŲYDcr# £a]BsPb $2UxucZc(g̣gǙ'ay& ?X|9_Z+uZ+A4z-Z 7oWχ7\Ёpʔ,J_V$K*XSIrl' -|#b[߉b@*Óȿak2GvX l`_S_'GrIUTt<@,D[[4VCD FɓyR+$5`!kd j?WG,9%-D\vŵtK;ZrWYa%6b:z;f 8 }v~s {yCԣzXz` ~\G\ώ~0ߦy_:_cOǮNIb'?ʓg|z>}}Ws5X;KSIR>Kj?_7>a>L<`:SxKZ>Aeۈy^Gܙn}9>q>~wrm,՞=ݿz3~U{m\ك=3 .n):t XRYØe0μ1#ơG^+'FF_ 5`N\RgONsDiAu8H=yCK+ ̩JнzO8i坡c-QO\Q9U6Icv?oI!ic۟~a2NNw51ۤbb}IFGx󽑊}5miw~@"ͱK'lPBUhv8N~z( VDlcwž;l[0z'~ eg=g+_>_۶0h<+͒Cᘓb㪻Y1`WioWyb@Uo_ho"53 b/0&CKB|3O~GT<1Gl|9':.UlLڭCo[x4$3)j#w.#|W=d|p]µAխU]W A5TʪD{(z嫢 zd_!\j}^!l9iؘ1G_nA2)89=xzzQ월b=iYl?r R:=$r{_/5t?DuUIo6"EoSpµ#M=Rn@]*?:U;C*L  vDE]LpH*)J $rïYWϞ=x+i/lĦ[.ډl~> 3?=42[՘\P;ڣI"hɆ}^-¢$OjfYxNxlCXAKe-۩ۤ}hE <H/e2`߄mK]ZCw%'jc8.FE'Ά=1Jy7b}096Ҙ&y9=Qb(z²_D>m@~-ˢLyͼȶtFpS Y_3.VqLuisó~ܣW76˫s s AHw|ŝ [9wLTrLL/`Lk%v~ 6Y<$} | Zӑ7ٖOZiG[rNqϤxN]c=0&pAEV?wC5A8NnYqViX 3oUiZ;8&ě{wXagĈe=a\O:<0-l}4[ |ؾfٔ/1 !nPF}z=# ԻO1o:1:"+|J]>.r喉oc nbXQfn@ީ2%ի5.Ɖ=v肱+m]SGp,7+td<薇 u3Y>yC}<nHY>QW>/yoiR+?|M)ΣJ}ϣ'OѣJ'zw0Qr?Yytϣ9>֕VQxS5'a3(u^&!-"s(^}_#~S|Z L묑+$wG|}W59UJ"}|E*E.fP~o%>BsYzdpP PJem%QVz|Wekc `{k;060f@7ujߤz%oz2xx^N<)`>sPe1ȵ?PGye:lY~Klp&{eAnȰ'fdXa+,wr{ng oy#pǼNX1XGe:!'r}zv"A}l_Ƒ_hLG=U4>+Q"zօv&JY_Qc%A'tSR-f<~M_p|AVpjgօuN:n(;Fn͟/#Ey~~@rS2哇qOngI?,º".܂雋=N#^W1ZoJ.Ǘx%x+}mZ }: gR|gPe@#AЁzz@yhDzMȤL<ӯ μ9/4gdas}B2~?WU qḐjinx bYлM˾mZBe}G }YQDE"V 7olԿqO; xU5A.&d̹U_#֮_#"UY967}p09iixϺNB1~KC޺<8Я2k58#lnƃsCiPGElw MR '=fskߠ`}Wר[.c=:{[ 6&&Ԥ{(=ytȣ'v!)2Lz9'vsya^˂U0AKeOcv{ vvmL+{Uwp5A8& wO- {WRf~ *X78!{ nFޏw=֏m7xR1|cz@g>9ǴА\RG@ x#nϲ,q[6yg6ٟ?X jc? F=|zGnc} -/5x g @OoYxbN#>B~[Ch3KGE][?5Ԩ#h(S Ô X>[@ s.2ȁ`[9-t ~pВG&2|ގe^ĵjWiE2Nܫ=%~JpOM{r iڀ"؟D2:OE?Z:jT,,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:02 15:37:49 60 UDC 541.138:535.379 IRINA B. SVIR* , NATHAN S. LAWRENCE, RICHARD G. COMPTON DIGITAL SIMULATION OF DIFFUSION PROCESSES AT A MICRODISC ELECTRODE In this paper we demonstrate that alternating direction implicit (ADI) method, in combination with the Amatore transformation of R and Z coordinate, gives a fast, efficient solution to the two-dimension (2D) non-steady state diffusion problem at a microdisc electrode. We describe the ECE reactions with second order kinetics and reagent restricted C step and compare simulation results with experimental data. 1. Introduction The microdisc electrode is by far the most popular microelectrode geometry as reflected in the volume of electrochemical literature published [1, 2]. The transient response of the microdisc electrode has been the subject of many studies [3]. There have employed a wide range of analytical, semi- analytical and finite-difference numerical methods to model a fairly narrow range of predominantly first-order chemical mechanisms (E, CE, EC, EC ’ , ECE, DISP1 and EC 2 E). The problem of numerical simulation of the current to a microdisc electrode is made difficult by the presence of a boundary singularity at the electrode edge, which causes large errors in the simulated concentration values, and consequently in the simulated flux at the electrode. Recently, Gavaghan [4-6] used the fully implicit finite-difference algorithm with the Richtmyer modification (the FIRM algorithm) and ADI with the exponentially expanding mesh for steady state diffusion problem of linear sweep voltammetry and chronoamperometry at microdisc electrode. Several simulation methods have been suggested to deal with such singularities for these various electrochemical problems. Crank and Furzeland [7], Gavaghan and Rollett [8], Galceran et al. [9] used a locally valid series expansion, Taylor et al. [10] used a mesh refinement technique based on a coordinate transformation, whilst Michael, Wightman, Amatore et al. [11- 13] and Verbrugge and Baker [14] have used a coordinate transformation, which effectively removes the singularity by “ folding ” the radial axis at the disc edge. Evans and Gourlay [15] used a locally valid series expansion in calculating the flux, but made no attempt to correct the concentration values. There have also been a large number of analytical approximations for these problems (for example [16-23]). * Corresponding author: svir@kture.kharkov.ua xoLUuǟsĿ+ v#&jHNE!KX4UbӥsaXR.s-ʱe@0F/pKmmn(^ s'cmml}=?9s~l""iYD\cB"&eD2͸>˃qJG8Fp66&x*i6IiW|B{V^W.k_kUd'Q;C?(Zi9?= ޸cLWٺrN.w -2\!V(%O<CJS/IBc #4P܈Mm7f_zo~+)=qm J &=%Y<ؿ#7%SʌL 5R,NYWYA̗vu n@' 0G6VB1 ¥pb_Up,Cmm0j?è l2O6S|j/y$cI:})>QEȇ4v &T~#G<,rɐ0 z*ƍv71thWǍkH~W,mPF/ m_ߢհgo )k{K03H:r'o7X QX7p=߂T^T#V߉ryH>gd7C H /3F7AsZ/'aNM̗]&0M&ZYe)\ȋQʉW±v9s8;CǩY?ved|{FQ~^AP&V5jDំ. {xH=d$.{iu 9T }נ I$9Cx>{hwӦ.D#'{~7[D`ΉBh*@N fM<Мk39EԳ]MmD5H|x?BG2oQF$=Rs}1ujDG8]kW>|  'K;R=IEZ;%ws=܁Z4&gy&8UzN1=/Cҳ3W[[j75sg>oL3h{ycoh?;yb3眚;̙Sǘ)_clƎ5w~s.qcO,9bor6so15_b]V X*`UU}uY*`UUV&*I "   V(162L/ `1 6{@x] `]E>iKKVR)4l)[B%l ]m -`P (A#T ,j /5꫊ {yܹח涓Μ9̜sW "!"Q]lj Z_8R@.[dbOܳ/- g/$3d)Ke$H5@\"k4l:-ҟ`"a8^K~a#c҈\%ȡ_ a QSLROE1UHA@` tJ:QH^`k'ΥC4w3X$Qa4k^fKOZ+`U2cc 9{"#$yr;Jn6ac#:4tФ+f\qBYtLHP :΍@a;-tʡ]؁W &ƊMGx\Eu" .E׷H*1BRRWrcM?ljJz+(Φ|$qO"A6I㵚!2uŐOE4/Ε $Yɒ9V?u:G%˃dzWes L1V0esX+.=axL<xNDlAW6_DMƔM6$WlfS `@_BLlV" TdEԝ(;A7sJbH\YfU!2|LQϕl,D|V9, ,vˀDLrSֺXݵ{ MvD>=v 5!,}eL,cĶSO!c{3Gqq_" h{M B|䵉czߙy`_Jݞ+ȳ Pʕ׬@l~u@v} %|m'VSryA.(_*9gh?_E+(sWѶ:v9z\&q2c#MHۘ^Ly#] rƬ#U&oXG\r=P&BY&, k(yB{:yBU*=w̵i;92p. ϵ3גyS9qn|sc])J6kPgwγ#O8\Mzr͵rz$ (.}1f_L8`b}RMNBhuwфs"ψ1Ǡk)˘'8vΓ|`LX]_9vΙeD_J~)ƺkj5u0Ԭ!.Ɗ\SE6/"@ƶ5@>`9HDc!{Wdu UVٛIs:BJxtfij6}}nWfuI Tܸ:΍z~'!!T86m-2_ΟzEZ_NҵE~P?20ccYOzf3lk'!>P2uK}~ N{^0@:b1ide0c(w<77CO!)xDz?+_"s_|]ugG ")_CtoCCG_vwzpFW1uH} ]cy_ʇf|U o8+ǵС0f;?omO[[vc&_ǀ|0_Io+yJ76v½6 Xlp&26) n W8;}8 O 0r<믫s»8rw$q\M[ mcl&wl7Pc>Ȯ.9Jz@>yF9)Ͼ:bυsٟXʨS̋yB!q?8^33ԟ>7ϤYǾ os#qtӳbM(Bڜ"ddL%gքqo}:6DNvsjÿuyO.َǹ%Pcp5+/I" ˇyi{Yf֛|zyq#p.>ZnҶDݑa̼Jo}wA;O$8sN,\y0 1͘8 \@ P{Jmzx7H; Α1,c=ӌY9`ֱ=aXΘy ˶+-Ow1 Aºzb%K".968ΕaΑ3fL ,f"<@e1X 6eE{x)y[س^:.,czʦ֩MJegK|~1?><=>2|AT){wv4K%bz;Us5tgOU'@bs!f`u!OY4a ,g[۫L}mva;қka8ֳc$c±1%SǸ<}Y o baZcye"|t.|;O.w!ʛtXgǸϝ׳sdKuc߼k]ÖǀAX4ø_u);yIǏѴUf?m{Av~j|[U/;{"=zu=KO; ~vW7k./+Gg˚c߮u)_qM6v)grR3Kmu xoekU˃zJXawqrk]rA\+Dž4oOvcA/?OzJYZ5 O۫f/WYi^&51B86m(@|c؀xbY7 e7eD_p?lCy~Y[&[b^gB>2P,wEXGl2q+ lιio`_nwE3EԕܟƦ9w+uq? 6g c/Aų_Y7d,:M{}?vq/!l1Q W"d~4+ϗP==:*F=T<{?P,G-+q֦83=Oq?v`r*UH2S>R~yM <ЫG ng8[tŲt0+Dž}9vU33tVSrPYi^ii0X?{^B7\`\Q|nKy~_27o[9W??༷wU3y p6\M뉍_u* lιio`_|!lg;ב8Wf#+349vۙ 3˦_Wc=Px񘪗qJ2q|g.WO_=Q |TOpSS>輻ʯHْm,=?ӺJz]f?2w~™46o8*.6@}¾zc;*ۙ*Oz+) ƞnV{ڟ׾?kc0  >CL.DVs pW-W(~3 :60ā+Mobz :|t GV;ܲHԟȔ+^u]_@}Y??ۿ)Col2=S%8ٿgL߆qa_8}}8"y3xGq_Qs vݟvoL/?@Muu@4q`^BšCD׸Hst?S5=2=`֘(SOE5~)O:|%K]iTk}>lg≣).RXjڥ\™v'  |Krc;p*'+ʋ^QiGN8L7p v/خLrBzA@SGM(ծS{ϟ׾Ghcfy~uq8{g@5I+ʫkmگ[`&z6u-~%u7Kn߳<߱_a?HMuZmiN]08 "/lι9.O1f_dr_EkGu*٦g+y7Ɯ+3)]b>l5롍_Jcd,:_ Vvέ=jzjs.ILWOO6EOM\cl+=Kz ~2.>ؗoVQ_QtjaS34a)yj-x4P\{ W8#;8߇v!EFa5KE/߰5Xg#(_)?؟^[ O}5jOs4e` ߑ'>&"YG˦#m0_ߒpn=ʦֆE+#_2yj~߱]h_je&@3~Tb|7w=A-[^ ){c2OꢖeXNiжe9c ^&VӾY}h{xZSŚ1P܌q߃ߣAtZρ\\ d"^4W@Y=PN"'"H\^H:=S#=43h֏۪k Y3l~n_?Ø=k,{RY?<m;ӓދ^΃Ňns/;b7pG|ps A;p|S |@ (e{1;hQ}Fw FFC:_-r쇌*9&9v^&Y)ClHo+SϊfZx<`Uo 4ᮃE-p58G5{'֦a_ie3AپL4[2ʴ{r;n\ZCcugțYEu6_Eck/_G W'd͙. 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The only difference is that in the former, the co- ordinate transformation does not involve an adjustable parameter. The Amatore and Fosset transformation [13] of space co-ordinate (Fig. 2) is ; 2 tg Z ; 2 cos 1 R 2                       (9) where d d r z Z ; r r R   . The system equations in transformed space co-ordinate (   , ) represents                               a 2 a 1 a G T a 2 2 2 2 2 , (10)   x b k b 2 b 1 b G T b 2 2 2 2 2                                , (11)   x b k x 2 x 1 x G T x 2 2 2 2 2 1                                , (12)   x b k c 2 c 1 c G T c 2 2 2 2 2                                , (13) where 2 d e c 2 d e b 2 d e a r T D r T D r T D        ;             2 tg 1 2 2 ;           2 cos 4 G 2 2 ; e bulk 2 T ] A [ k k   , where e T is the electrolysis duration. Fig. 2. 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(15) 4. Experimental All reagents were obtained from Aldrich and were of the highest grade available and used without further purification. All solutions and subsequent dilutions were prepared using deionised water from an Elgastat (Elga, UK) UHQ grade water system with a resistivity of not less then 18 MOhm cm. Solutions were prepared by dissolving the appropriate analyte in pH 4 acetate buffer (0,1 M). In general, all the solutions were degassed and stored under Argon with the DMPD being kept in the dark due to its photosensitivity. Stock sulfide solutions (0,05M) were prepared by dissolving S Na 2 in previously degassed NaOH (25mM) and were used within one hour of preparation to minimise losses due to aerial oxidation. Electrochemical measurements were recorded using an Autolab PGSTAT 30 computer controlled potentiostat (EcoChemie, Netherlands) with a standard three electrode configuration and a typical cell volume of 40 cm3. Three microdisc electrodes (BAS Co., Tokyo, Japan) with nominal radii ranging from 3,5 to 12,5 microns served as the working electrodes, platinum wire wound into a spiral provided the counter electrode with a saturated calomel reference electrode (Radiometer, Copenhagen) completing the cell assembly. The microelectrodes were carefully polished using 1,0 and 0,3 micron alumina before use. The microelectrodes were electrochemically calibrated prior to use to obtain an accurate measurement of the electrode diameters. This was carried out in a solution containing 2,12 mM ferricyanide ( 1 2 9 s m 10 76 . 0 D     ) in 0,1M aqueous KCl with linear sweep voltammograms recorded for each electrode. 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Results and discussion A system which has been shown to follow the mechanistic scheme involves the mediated oxidation of hydrogen sulphide (X) using N,N- dimethyphenylenediamine (A) in aqueous solution at platinum electrodes [24]. The main parameters from experiment: the bulk concentrations [A] bulk , [X] bulk where [A] bulk  [X] bulk  200 mM; diffusion coefficients: D A = D B = D C = 9 x 10 -6 cm 2 s -1 ; D X = 1,64 x 10 -5 cm 2 s -1 ; constant of rate: k 2 = 8 x 10 4 mol -1 dm 3 s -1 ; radius of microdisc electrode: r e = 3,5 mm  30 mm . The coefficient of efficiency is ) 0 k ( Current Current N 2 eff   (16) as a function of k 2 and  . Fig. 3. N eff for microdisc diameter = 7,3  m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 X bulk A bulk 1.025 1.05 1.075 1.1 1.125 1.15 1.175 N f f e 2 1 Fig. 4. 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The difference between calculated results and experimental data follows from the different electrolysis conditions: in our digital simulation we have non-steady state electrolysis, while experiment demonstrates steady-state. Our conclusion that the alternating direction implicit method, in combination with the Amatore transformation of R and Z coordinate, gives a fast, efficient solution to the two-dimension (2D) problem of non-steady state diffusion problem at a microdisc electrode. The obtained graphics shows this fact for digital simulation of ECE reactions with second order kinetics and reagent restricted C step. All programs were written using the Delphi 5 and executed on PC with Intel Pentium II 350 MHz processor. All codes are available from the corresponding author on request. Acknowledgements We thank The Royal Society of United Kingdom for grant of Joint Project between the group of Professor Richard G. Compton (Oxford University, Theoretical & Physical Chemistry Laboratory) and the group of Dr. Irina B. Svir (Kharkov State Technical University of Radioelectronics, Mathematical & Computer Modelling Laboratory). References: 1. A.M. Bond, Analyst. 119, (1994), R1. 2. J. Robinson, Comprehensive Chemical Kinetics, 29, (1989), 155. 3. J.A. Alden, F. Hutchinson, R.G. Compton, J. Phys. Chem. B, 101, (1997), 949. 4. D.J. Gavaghan, J. Electroanal. Chem. 456 (1998) 1-12. 5. D. J. Gavaghan, J. Electroanal. Chem. 456 (1998) 13-23. 6. D. J. Gavaghan, J. Electroanal. Chem. 456 (1998) 25-35. 7. J. Crank, R.M. Furzeland, J Inst. Maths. Applic. 20 (1977) 355. 8. D. J Gavaghan, J.S Rollett, J Electroanal Chem 295 (1990) 1. 9. J. Galceran, D.J. Gavaghan, J. S. Rollett, J Electroanal Chem 394 (1995) 17. 10. G. Taylor, H.H. Girault, J. McAleer, J. Electoanal. Chem. 293 (1990) 19. 11. A.C. Michael, R.M. Wightman, C.A. Amatore, J. Electroanal. Chem. 267 (1989) 33. 12. I. Lavagnini, P. Pastore, R. 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Îñê³ëüêè ïåðåë³÷åíi âèùå ïðèéìà÷i iíôðà÷åðâîíîãî âèïðîìiíþâàííÿ íå äîçâîëÿëè îòðèìàòè çîáðàæåííÿ áåç ñêàíóþ÷îãî ïðèñòðîþ, à êîíñòðóêöiÿ îñòàííüîãî äîñèòü ñêëàäíà ÿê ó âèãîòîâëåííi, òàê i â åêñïëóàòàöi¿, áóëè çðîáëåí³ ñïðîáè ïîáóäóâàòè òåïëîâiçiéíèé ïðèëàä áåç ñêàíàòîðà. Ïåðøèì íåñêàíóþ÷èì òåïëîâiçîðîì ìîæíà ââàæàòè åâàïàðîãðàô, â ÿêîìó ðiçíèöÿ òåìïåðàòóð îá ’ ºêòà i îòî÷óþ÷îãî ôîíó ïåðåòâîðþºòüñÿ â ðiçíèöþ òîâùèí ìàñëÿíî¿ ïëiâêè, ÿêà âèïàðîâóºòüñÿ â ïðîöåñi íàãðiâó. Âñi êîíñòðóêöi¿ åâàïàðîãðàôiâ íå çíàéøëè øèðîêîãî çàñòîñóâàííÿ, áî âèìàãàþòü âèïàðóâàííÿ ìàêðîñêîïi÷íî¿ êiëüêîñòi ðåºñòðóþ÷î¿ ðå÷îâèíè. Îïèñàíi íèæ÷å äîñëiäè ïîêàçàëè, ùî ìåòîäîì õåìîãðàôi¿ [1,2] òàêîæ ìîæíà âiäîáðàçèòè õàðàêòåð òåïëîâîãî ïîëÿ ÷åðåç âiäïîâiäíó éîìó iíòåíñèâíiñòü ôîòîàêòèâíèõ ìîëåêóëÿðíèõ ïîòîêiâ [2] ç ïîâåðõíi òâåðäîãî ò³ëà, ÿê³ ðåºñòðóþòüñÿ çà äîïîìîãîþ ôîòîïëàñòèíêè. Íà ñòà䳿 ÿê³ñíèõ äîñë³äæåíü òåõí³êà ïðîâåäåííÿ åêñïåðèìåíòó íå âèìàãຠñêëàäíîãî îáëàäíàííÿ. Ïåðøi ñïðîáè ðåºñòðàö³¿ òåïëîâîãî âèïðîì³íþâàííÿ áóëè ïîâ ’ ÿçàíi ç êîíòàêòíèì íàãð³âîì òà áåçïîñåðåäíiì îïðîìiíåííÿì ïîâåðõíi òâåð- äîãî ò³ëà, çîêðåìà êðåìíiþ. Ñôîðìîâàíå çà äîïîìîãîþ îïòè÷íî¿ ñèñòå- ìè çîáðàæåííÿ òåïëîâîãî äæåðåëà íà ïîâåðõíi âèêëèêàëî ¿¿ íàãðiâ, i ÿê íàñëiäîê - ìîäóëÿöiþ iíòåíñèâíîñòi ôîòîìîëåêóëÿðíèõ ïîòîêiâ ç ðiçíèõ äiëÿíîê êðåìíiþ âiäïîâiäíî äî ñóìàðíîãî ïîòîêó òåïëîâî¿ åíåðãi¿ íà êîæíó ç íèõ. Iíøèìè ñëîâàìè, ïiñëÿ îïðîìiíåííÿ ðiçíi äiëÿíêè êðåìíiþ áóäóòü ìàòè ðiçíó õåìîãðàôi÷íó çäàòíiñòü. Òåïëîâå çîáðàæåííÿ íà ðèñ. 1 îòðèìàíå áåçïîñåðåäíüî ôîêóñóâàííÿì òåïëîâîãî âèïðîìiíþâàííÿ ëàìïè ðîçæàðþâàííÿ íà ïîâåðõíþ êðåìíiÿ. Ïîòóæíèé òåïëîâèé ïîòiê (100 Âò) ðîçiãðiâàâ ïîâåðõíþ ïëàñ- òèíêè êðåìíiþ, ïðèñêîðþþ÷è ¿¿ îêèñëåííÿ, i çìiíþâàâ òèì ñàìèì ¿¿ ðåàãåíòîçäàòíiñòü. Íåäîëiêîì çàçíà÷åíîãî ìåòîäó º íåìîæëèâiñòü ðåºñòðóâàííÿ ñëàáêèõ òåïëîâèõ ïîòîêiâ ÷åðåç âèñîêó òåïëîïðîâiäíiñòü êðåìíiþ, ÿêà ïðè- çâîäèòü äî çíà÷íîãî ðîçñiþâàííÿ òåïëà. Äëÿ çìåíøåííÿ òåïëî- ïðîâiäíîñòi ÷óòëèâèé åëåìåíò â ñåði¿ íàñòóïíèõ äîñëiäiâ âèãîòîâëÿâñÿ ÿê ìîçà¿÷íà ñòðóêòóðà ç îêðåìèõ çåðåí êðåìíiþ, àáî ó âèãëÿäi ñóìiøi ïî- ðîøêà êðåìíiþ i â ’ ÿæó÷î¿ ðå÷îâèíè (íàïðèêëàä, åïîêñèäíî¿ ñìîëè). Öå äîçâîëèëî ïiäâèùèòè ÷óòëèâiñòü åëå- ìåíòà ïðèáëèçíî íà ïîðÿäîê i çà- ðåºñòðóâàòè ìåíø ïîòóæíèé òåïëî- âèé ïîòiê (5 Âò), ñôîêóñîâàíèé íà éîãî ïîâåðõíi (ðèñ. 2). Ðèñ. 1. Âïëèâ íà õåìîãðàô³÷íó ðåàãåíòîçäàòí³ñòü ïîâåðõí³ çðàçêà êðåìí³þ òåïëîâîãî îïðîì³íåííÿ. Åêðàíîâàí³ ä³ëÿíêè íà ôîòîãðàô³¿ ñâ³òë³ xLu?8qRH 7;Z km&YjjlVe-lb昫!Ks[".&ca_PGCcctmoߟ/>=_؎}PnNP/'ef;z rWwPk9W,t20 Z?s}^it1E=Wr[08G^s9nrN#ba}3 ߆49ԅ67T2s%9ZM[ҨD߀^%l.%S|V#y;R`EZ鷀~!N/4_&o\<{tu{  4T WX:B(16J2/1$B%{ex @TB-(-(*@@n!)7()t|B|ޠ@  )VwYeu]e!;:3s|;3sa6{x|n= cuxh7C/. c$I00 F16^H0U 2S?x22&ye0kcu< { pc7looL?iD1{l < n,< 8I6|xc^ ?8ج7@+ |G#pYx-sp˗/3c7PD; b35Qgۊ5o^^a8„AϽ0&̟aAmq0`5YOǸwYDf.cy`P؛pttpϦA' p.gf1cN{m\ƌV3piY}죚=^4hzU_7[VXGrr ʉa^nȣa=Wac~⵰nW<f`}. 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