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Логические системы в различных функциональных наборах и их реализация

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Ainoaea?noaaiiue eiieoao ii ia?aciaaieth ?inneeneie Oaaea?aoeee

Iineianeee einoeooo ?aaeeioaoieee, yeaeo?iieee e aaoiiaoeee

oaeoeueoao eeaa?iaoeee

eaoaae?a eioaeeaeooaeueiuo oaoiieiaee e nenoai

a?oiia E?-1-95

Oaia:

«Eiae/aneea nenoaiu a ?acee/iuo ooieoeeiiaeueiuo iaai?ao e eo
?aaeecaoeey»

Eo?n:

«Oai?aoe/aneea iniiau eioi?iaoeee»

Caaeaiea ? 29.419, 7.942, 26.345

Nooaeaio: Eaieoia E.I.

?oeiaiaeeoaeue: Nai?iia A.E.

@( «EEI«

@( Eaai Eaieoia

Iineaa 1997Caaeaiea ia eo?niaia i?iaeoe?iaaiea ii eo?no:

«Oai?aoe/aneea iniiau eioi?iaoeee»

Nooaeaioa: Eaieoiaa E.I. a?. E?-1-95.

Oaia: «Eiae/aneea noaiu a ?acee/iuo ooieoeeiiaeueiuo iaai?ao e eo
?aaeecaoeey»

1. Enoiaeiua aeaiiua

1.1. No?iea ec oanoiaaeoeaoe neiaieia A = { a0,a1, …, a15 }

Iao?e/iue eiaeeeaoi? 5 ( 7 = 35 y/aae.

Iiiaeanoai i?eciaeia H = { h0,h1, …, h35 }

Oneiaea oi?ie?iaaiey no?iee neiaieia e ioia?aaeaiey T:H
( A ( F.

I?aaeei auaeaeaiey OAE ec aeaiiuo ioieoa 1.3.

Eioaa?aeueiue iaai? E155 (ii ni?aai/ieeo)

Oneiaea oi?ie?iaaiey iiaei?ino?ainoaa O NIAeA?AEAIEA TOC \* MERGEFORMAT Aaaaeaiea. GOTOBUTTON _Toc386455996 PAGEREF _Toc386455996 4 1. Enoiaeiua aeaiiua. GOTOBUTTON _Toc386455997 PAGEREF _Toc386455997 5 1.1. No?iea ec oanoiaaeoeaoe neiaieia. GOTOBUTTON _Toc386455998 PAGEREF _Toc386455998 5 1.2. Iao?e/iue eiaeeeaoi?. GOTOBUTTON _Toc386455999 PAGEREF _Toc386455999 5 1.3. Oi?ie?iaaiea ioia?aaeaiey no?iee neiaieia. GOTOBUTTON _Toc386456000 PAGEREF _Toc386456000 5 2. I?iiaaeooi/iia enneaaeiaaiea enoiaeiuo aeaiiuo. GOTOBUTTON _Toc386456001 PAGEREF _Toc386456001 6 2.1. Ioia?aaeaiea neiaieia no?iee A ia eiaeeeaoi?a. GOTOBUTTON _Toc386456002 PAGEREF _Toc386456002 6 2.2. Iieo/aiea OAE GOTOBUTTON _Toc386456003 PAGEREF _Toc386456003 7 2.3. Iaoiaeaeaiea iiia?ia OAE ii ea?oa Ea?ii GOTOBUTTON _Toc386456004 PAGEREF _Toc386456004 9 2.4. Oaaeeoea enoeiiinoe. GOTOBUTTON _Toc386456005 PAGEREF _Toc386456005 9 2.5. I?aaenoaaeaiea OAE a niaa?oaiiie ii?iaeueiie oi?ia. GOTOBUTTON _Toc386456006 PAGEREF _Toc386456006 10 2.6. Ieieiecaoeey OAE GOTOBUTTON _Toc386456007 PAGEREF _Toc386456007 11 2.7. I?aaenoaaeaiea OAE a aeaea eoaa GOTOBUTTON _Toc386456008 PAGEREF _Toc386456008 12 3. Enneaaeiaaiea OAE. GOTOBUTTON _Toc386456009 PAGEREF _Toc386456009 13 3.1. Iao?eoea ioiioaiee. GOTOBUTTON _Toc386456010 PAGEREF _Toc386456010 13 3.2. Enneaaeiaaiea OAE ia oiea?aioiinoue. GOTOBUTTON _Toc386456011 PAGEREF _Toc386456011 13 3.3. Enneaaeiaaiea OAE ia yeaeaaeaioiinoue. GOTOBUTTON _Toc386456012 PAGEREF _Toc386456012 14 3.4. Iao?eoea yeaeaaeaioiinoe e oiea?aioiinoe. GOTOBUTTON _Toc386456013 PAGEREF _Toc386456013 14 3.5. Aeeaa?aiia Yeea?a. GOTOBUTTON _Toc386456014 PAGEREF _Toc386456014 15 3.6. Iino?iaiea eiiaeiaoeeiiiie noaiu. GOTOBUTTON _Toc386456015 PAGEREF _Toc386456015 16 Nienie eniieueciaaiiie eeoa?aoo?u GOTOBUTTON _Toc386456016 PAGEREF _Toc386456016 17 Caeeth/aiea GOTOBUTTON _Toc386456017 PAGEREF _Toc386456017 17 Aaaaeaiea. N ?acaeoeai yeaeo?iieee i?eia?aoatho ia?iiiia cia/aiea yeaeo?iiiua aecoaeueiua n?aaenoaa ioia?aaeaiey eioi?iaoeee. Yoe n?aaenoaa i?aaenoaaeytho niaie ?aciiia?aciie aaee/eiu ye?aiu, ioi?ieaiiua ?acee/iuie niiniaaie (oeeoa?aeaou /ania, oaaei ia noaaeeiiao e o.ae.) O anao yoeo n?aaenoa iauay aeaoaeue - yeaiaio, ioia?aaeathuee oieueei iaeei neiaie. Yoe yeaiaiou i?aaenoaaeytho niaie iao?eoeo, a eeaoeao eioi?ie niiioe?iaaiu naaoyueany yeaiaiou (eaiii/ee e o.i.) I?e iiaea/a ia ieo iai?yaeaiey, ioia?aaeaaony oio eee eiie neiaie aecoaeueiie eioi?iaoeee. Oaiie aeaiiiai eo?niaiai i?iaeoa yaeyaony ?ac?aaioea aaoiiaoa, oi?aaeythuaai naaoyueieny yeaiaioaie, aeey ioia?aaeaiey iaiaoiaeeiiai niiauaiey ia oaaei. Eaaeaeue neiaie niiauaiey ioia?aaeaaony ia ioaeaeueiie iao?eoea (iao?e/iii eiaeeeaoi?a) 5 ( 7 naaoyueony yeaiaioia, oi anoue eaaeaeiio neiaieo niioaaonoaoao ii?aaeaeaiiay eiiaeiaoeey naaoyueony yeaiaioia iao?eoeu. A aeaiiii eo?niaii i?iaeoa ioaeii aua?aoue o?e i?eciaea (naaoyuaainy yeaiaioa) e iino?ieoue aaoiiao, oi?aaeythuee yoeie i?eciaeaie i?e iiaea/a ia aoiae /aou?ao?ac?yaeiiai oi?aaeythuaai eiaea. Aeey ?ac?aaioee aaoiiaoa iaiaoiaeeii i?iecaanoe aiaeec ia oiea?aioiinoue e yeaeaaeaioiinoue. A caeeth/aiea iaiaoiaeeii naeaeaoue auaiae. 1. Enoiaeiua aeaiiua. Enoiaeiuie aeaiiuie yaeyaony no?iea ec oanoiaaeoeaoe neiaieia, a oae aea iao?e/iue eiaeeeaoi?, iacia/aiea eioi?iai aoaeao iiae?iaiaa ?anniio?aii a ioieoa 1.2. 1.1. No?iea ec oanoiaaeoeaoe neiaieia. No?iea ec oanoiaaeoeaoe neiaieia auae?aaony i?iecaieueii. Iia yaeyaony iauaeoii enneaaeiaaiey. A aeaiiii eo?niaii i?iaeoa eniieuecoaony no?iea, i?eaaaeaiiay ia ?enoiea 1.1. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 E A A I I E O A E E I A E * . ?en. 1.1. No?iea ec oanoiaaeoeaoe neiaieia 1.2. Iao?e/iue eiaeeeaoi?. Iao?e/iue eiaeeeaoi? - iao?eoea ?acia?iinoueth 5 ( 7 = 35 y/aae. N iiiiuueth iao?e/iiai eiaeeeaoi?a iiaeii ethaiio neiaieo (aoeaa, ciaeo i?aieiaiey, oeeo?a e o.ae.) iinoaaeoue a niioaaonoaea iaai? i?eciaeia H = { h1, h2, ..., h35 }. Aiaoiee aeae iao?e/iiai eiaeeeaoi?a i?aaenoaaeai ia ?enoiea 1.2. ?en. 1.2. 1.3. Oi?ie?iaaiea ioia?aaeaiey no?iee neiaieia. N iiiiuueth iao?e/iiai eiaeeeaoi?a onoaiaaeeaaaony niioaaonoaea eaaeaeiio neiaieo ai ec enoiaeiie no?iee neiaieia A (ni. i. 1.1) ii?aaeaeaiiue iaai? i?eciaeia Ia Iaoiaeaeaiea iiia?a OAE: F3 N(F3) = 21 + 22 + 212 + 28+ 29 + 210 + 211 = 7942 Iaoiaeaeaiea iiia?a OAE: F5 N(F5) = 20 + 23 + 25 + 26 + 27 + 29+ 210 + 213 + + 214 = 26345 2.5. I?aaenoaaeaiea OAE a niaa?oaiiie ii?iaeueiie oi?ia. I?aaenoaaei aua?aiiua i?eciaee a niaa?oaiiie aeecuthieoeaiie ii?iaeueiie oi?ia (NAeIO) e niaa?oaiiie eiiuthieoeaiie ii?iaeueiie oi?ia (NEIO). Aeey yoiai ec oaaeeoeu enoeiiinoe OAE (ni. oaae. 2) auieoai eiinoeooyiou 0 e 1. OAE a NAeIO i?eiao aeae: F1(X,Y,Z,P) = (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) F3(X,Y,Z,P) = (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) F5(X,Y,Z,P) = (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) ( (X,Y,Z,P) OAE a NEIO i?eiao aeae: F1(X,Y,Z,P) = (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) F3(X,Y,Z,P) = (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) F5(X,Y,Z,P) = (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) & (X ( Y ( Z ( P) 2.6. Ieieiecaoeey OAE I?iaaaeai ieieiecaoeeth iieo/aiiuo OAE i?e iiiiue ea?ou Ea?ii e i?aaenoaaei eo a AeIO. Aeey yoiai iiiuoaainy iioeiaeueiui ia?acii iauaaeeieoue 0-eoau a eoau aieueoae ?acia?iinoe. Eeaoee, ia?acothuea k-eoa, aeatho ieieoa?i n-k ?aiaa, aaea n - /enei ia?aiaiiuo, eioi?ua nio?aiytho iaeeiaeiaia cia/aiea ia yoii k-eoaa. Oaeei ia?acii, iieo/ei AeIO aua?aiiuo OAE. ?en 2.2a ?en 2.2a ?en 2.2a I?iaaaeai ieieiecaoeeth aeaaa?ae/aneei iooai, ainiieueciaaaoenue oiaeaeanoaii a ( a = a. XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP = XYZ ( XZP ( XZP ( YZP ( XYZ ( XZP = ZP ( XYZ ( XZP ( YZP ( XYZ XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP( XYZP ( XYZP ( XYZP ( XYZP = YZP ( YZP ( XZP ( XYZ ( XYZ = XY ( YZP ( YZP ( XZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP ( XYZP( XYZP ( XYZP ( XYZP ( XYZP ( XYZP = XZP ( XYP ( XYZ ( XZP ( XZP ( XYZP 2.7. I?aaenoaaeaiea OAE a aeaea eoaa 3. Enneaaeiaaiea OAE. 3.1. Iao?eoea ioiioaiee. Iino?ieoue iao?eoeo ioiioaiee T:H ( A. Iao?eoea ioiioaiee i?aaenoaaeyao niaie oaaeeoeo, no?ieaie eioi?ie yaeythony caiene (ei?oaaee i?eciaeia), a no?ieaie ioiioaiey, eioi?ua eiatho ana oieeaeueiua eiaia. Iao?eoea ioiioaiey i?aaenoaaeaia a oaaeeoea 3. Iao?eoea ioiioaiee. Oaae. 3 3.2. Enneaaeiaaiea OAE ia oiea?aioiinoue. Ii?aaeaeei eeannu oiea?aioiinoe. ?anniio?ei eeannu oiea?aioiinoe k1, k2, k3, eiathuea iauea yeaiaiou, neaaeiaaoaeueii, yaeythueany ia?anaeathueieny iiiaeanoaaie. h1 = h((1) = h(A) = { X0, X1, X3, X5, X6, X7, X9, X12, X13, X14 } h2 = h((2) = h(B) = { X1, X2, X8, X9, X10, X11, X12 } h3 = h((3) = h(C) = { X0, X3, X5, X6, X7, X9, X10, X13, X14 } I?iaiaeece?iaaa eeannu h1, h2, h3, iiaeii iieo/eoue: k1 ( k2 = 0; k1 ( k3 = 0; k2 ( k3 = 0, o.a. {k1, k2, k3 } - ia?acotho eeann oiea?aioiinoe ?acoeueoaou enneaaeiaaiey caianai a oaaeeoeo 3. 3.3. Enneaaeiaaiea OAE ia yeaeaaeaioiinoue. Ii?aaeaeei eeannu yeaeaaeaioiinoe aeey yoiai iiiaeanoaa A = {O0, O1, ...., O15 } ?aciaueai ia eeannu yeaeaaeaioiinoe, iieo/ei 6 eeannia I1 = {AC} = {X0,X3,X5,X6 X7,X13,X14} I2 = {AB} = {X1,X12} I3 = {B} = {X2,X8,X11} I4 = { } = {X4,X15} I5 = {ABC} = {X9} I6 = {BC} = {X10} I?e yoii eaaeaeue eeann iieiinoueth ii?aaeaeyaony ethaui aai i?aaenoaaeoaeai. Niiinoaaea ?acoeueoaou enneaaeiaaiey n ?acoeueoaoaie ioieoa 3.2 iieo/ei neaaeothuea caaeneiinoe I1 ( K1 I2 ( K1 I3 ( K2 I5 ( K1 I6 ( K2 I1 ( K3 I2 ( K2 I5 ( K2 I6 ( K3 I5 ( K3 eee K1 = M1 ( M2 ( M5 K2 = M2 ( M3 ( M5 ( M6 K3 = M1 ( M5 ( M6 ?acoeueoaou enneaaeiaaiey caianaiu a oaaeeoeo 3. ?acoeueoaou enneaaeiaaiey ia yeaeaaeaioiinoue e oiea?aioiinoue iaiaoiaeeiu aeey iioeiecaoeee iino?iaiey eiae/aneie noaiu. 3.4. Iao?eoea yeaeaaeaioiinoe e oiea?aioiinoe. Iao?eoeo yeaeaaeaioiinoe e oiea?aioiinoe iiaeii i?aaenoaaeoue a aeaea eaaae?aoa, ii aeeaaiiaee eioi?iai no?iyony eeannu yeaeaaeaioiinoe, a caoai ono?aeaathony ioiioaiey oiea?aioiinoe. Iao?eoea yeaeaaeaioiinoe e oiea?aioiinoe i?aaenoaaeaia a oaaeeoea 4. Iao?eoea yeaeaaeaioiinoe e oiea?aioiinoe. Oaaeeoea 4. 3.5. Aeeaa?aiia Yeea?a. Aeeaa?aiia Yeea?a aeaao iaaeyaeiia i?aaenoaaeaiea i oii, eae ?ani?aaeaeythony i?eciaee ii eeannai oiea?aioiinoe e yeaeaaeaioiinoe. Aeeaa?aiia Yeea?a aeey aua?aiiuo OAE i?aaenoaaeaia ia ?enoiea 3.5. Aeeaa?aiia Yeea?a. ?en. 3.5 3.6. Iino?iaiea eiiaeiaoeeiiiie noaiu. Eiiaeiaoeeiiiay noaia aaoiiaoa ?aniiciaaaiey iaai?a i?eciaeia H = {h1, h3, h5 } iino?iaia ia iniiaa ?acoeueoaoia enneaaeiaaiee a ioieoa 3.1 e ioieoa 3.4. Oaaeeoea 5 Eniieuecoy oaaeeoeo 5, iiaeii caienaoue neaaeothuea ioiioaiey: G1 = (XYZP) ( (XYZP) ( (XYZP) ( (XYZP) ( (XYZP) ( (XYZP) ( (XYZP) = (XYZP) ( (XYZP) ( (XYZP) ( (XYZ) ( (YZP) G2 = (XYZP) ( (XYZP) G3 = (XYZP) ( (XYZP) ( (XYZP) G4 = (XYZP) ( (XYZP) G5 = (XYZP) G6 = (XYZP) Oiaaea OAE iiaeii i?aaenoaaeoue a aeaea: F1 = G1 ( G2 ( G5 F3 = G2 ( G3 ( G5 ( G6 F5 = G1 ( G5 ( G6 Yoe ioiioaiey yeaeaaeaioiu OAE a NAeIO, iieo/aiiui a ioieoa 2.5. Eiiaeiaoeeiiiay noaia no?ieeanue a aeaa yoaia: 1 yoai: - iino?iaiea eiiaeiaoeeiiiie noaiu ia yeaiaioao e, eee, (ianoaiaea?oiuo). 2 yoai: - caiaia ianoaiaea?oiuo yeaiaioia ia noaiaea?oiua e-ia Ieii/aoaeueiue aa?eaio eiiaeiaoeeiiiie noaiu i?eaaaeai a i?eeiaeaiee 1. Nienie eniieueciaaiiie eeoa?aoo?u 1. A.I. Neai?neee. «Iaoaiaoe/aneee aiia?ao eiaeaia?a» - ecaeaoaeuenoai Eeaa: Oaoieea - 1975 a. Caeeth/aiea I?iaaaey aiaeec ia oiea?aioiinoue e yeaeaaeaioiinoue, iu iino?ieee aaoiiao, ?aniiciathuee ei?oaae i?eciaeia H = {h1, h3, h5 }, eioi?ue ninoieo ec 16 - oe eiae/aneeo yeaiaioia. PAGE PAGE 17 «EEI«

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