Ee?anueeee oi?aa?neoao

?iai? Oa?ana Oaa/aiea

Iaaeaaae?a Ieoaeei Aaiiaae?eiae/

OAeE 681.3

Aeine?aeaeaiiy oa ?ic?iaea ia/enethaaeueieo noai, aaciaaieo ia
eiiooaoe?eieo aeaiaioao

01.05.03 – iaoaiaoe/ia oa i?ia?aiia caaacia/aiiy ia/enethaaeueieo iaoei
oa nenoai

aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a-1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? iaoaiaoe/ii? ?ioi?iaoeee oaeoeueoaoo
e?aa?iaoeee Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee — eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

Aeeaiaaoeue Ieeiea Ieeieaeiae/

Io?oe?ei? iiiiaioe:

1. aeieoi? oaoi?/ieo iaoe Oeaeoe?i Aai?a?e Ian?eiae/ (I?aeia?iaeiee
Nieiiii?a oi?aa?neoao, i?ioani? oaeoeueoaoo eiii’thoa?ieo iaoe)

2. eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio I?ioeaiei Aieiaeeie?
Naiaiiae/ (Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, aeioeaio)

I?ia?aeia i?aai?caoe?y — ?inoeooo E?aa?iaoeee ?i. A.I. Aeooeiaa IAI
Oe?a?ie, a?aeae?e oeeo?iaeo aaoiiao?a, i. Ee?a.

Caoeno a?aeaoaeaoueny 25 aa?aciy 1999 ?. ia can?aeaii? niaoe?ae?ciaaii?
a/aii? ?aaee Ae 26.001.09 Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana
Oaa/aiea, Ee?a, i?. Aeooeiaa, 2, ei?i.6, o-o e?aa?iaoeee, aoae. 40 i 14
aiaeei?. (Oae.252-58-83. Oaen 266-12-49, E-mail:
[email protected])

C aeena?oaoe??th iiaeia iciaeiieoeny o Iaoeia?e a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea, Ee?a, aoe. Aieiaeeie?nueea, 58

Aaoi?aoa?ao ?ic?neaiee 17 ethoiai 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee A.I.Oaa/aiei

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue i?iaeaie. ?icaeoie e?aa?iaoeee ye iaoee, aaeineiiaeaiiy
i?ia?aiii — aia?aoiiai caaacia/aiiy, noai?aiiy ??cieo e?aa?iaoe/ieo
aaoiiao?a a cia/i?e i??? aecia/athoueny aeinyaiaiiyie a iaeano?
ia/enethaaeueieo noai. No/aniee ??aaiue o?aaeeoe?eii? o?eaa?ii?
aeaiaioii? aace AII iaaeeceany aei iaeneiaeueiiai ii?iao iiaeeeainoae
naiai aeei?enoaiiy. I?ia?an a aoaeoeaiino? ia?iaee ?ioi?iaoe?? nooo?ai
i?aeaeueoe iiaeia oeyoii noai?aiiy iiai? aeaiaioii? aace ? iiaeo
aeai?eoi?a ?aae?caoe?? iniiaieo ia/enethaaeueieo ooieoe?e ia i?e, oa
iiaoaeiae ia oe?e aac? ooieoe?iiaeueieo noai iniiaieo oeeo?iaeo
i?eno?i?a – noiaoi?, oeo?aoi?, ioeueoeieaeni? ? oiio iiae?aieo.

Aeooaeuei?noue oeeo ieoaiue aecia/aa ua a nai?o ?iaioao A.I.Aeooeia.
Ieoaiiy ?aoe?iiaeueiiai eiino?othaaiiy aai neioaco noai oeeo?iaeo iaoei
c i?ia?aiiei ea?oaaiiyi A.I.Aeooeia ?icaeyaeaa a eiioaeno? neioaco
oeeo?iaeo aaoiiao?a, ine?eueee aeia?eueia AII ? i?eeeaaeii iaeiiai c
iaea?eueo iioe?aiiai oeio ia?aoai?thaa/?a aeene?aoii? ?ioi?iaoe?? –
aeene?aoieo aaoiiao?a.

Iaeiei c iniiaieo ia?aiao??a ?iaioe AII ? oaeaee?noue, yea ye i?aaeei
ca?eueoo?oueny aai ca aeiiiiiaith i?aeaeuaiiy ?ioaa?aoe?? noai, aai a
?acoeueoao? ca?eueoaiiy oaeoiai? /anoioe i?ioeani?a. Aea ca?eueoaiiy
oaeaeeino? oaeeie caniaaie ia iiaea a?aeaoaaoeny iane?i/aiii /a?ac
iaiaaeai? o?ce/i? iiaeeeaino?. A aeena?oaoe?ei?e ?iaio? i?iiiio?oueny
aeei?enoiaoaaoe a yeino? ?ino?oiaioa??th ?aae?caoe?? ia/enethaaeueieo
noai eiiooaoe?ei? aeaiaioe (EA) cai?noue eia?/ieo, ye? nueiaiaei?
neeaaeathoue iniiao iiaoaeiae oeeo?iaeo i?eno?i?a.

E?ieii i?aeaeuaiiy ia/enethaaeueieo iiooaeiinoae AII ? ?o ia’?aeiaiiy a
ia?aeaeuei? eiiieaene, ia?aae?. Iaei??th c iaeaaaeeea?oeo ooo i?iaeai ?
caaea/a ia?aaea/? aeaieo aai ia?o?ooecaoe??. Iniiaieie oa?aeoa?enoeeaie
a caaea/ao ia?o?ooecaoe?? ? /an ia?aaea/? ?ioi?iaoe?? oa e?euee?nia
ioe?iea aaciaeo aeaiaio?a, c yeeo neeaaea?oueny noaia ia?aae?.
Iioe?aieie oiiieia?yie ia?aae ia?aaea/? ?ioi?iaoe?? ? ?iciiae?eai? A?i?,
Iiaaa oa Aaia ia?aaea. Aaeineiiaeaiiy no?oeoo?e ?iciiae?eaieo ia?aae oa
iiooe iiaeo cania?a ?aae?caoe?? ni?ooth/eo ia?aae ? iaei??th c iniiaieo
caaea/ a ?ic?iaoe? cania?a ca’yceo aaaaoii?ioeani?ieo nenoai.

Aeine?aeaeaiiy aeena?oaoe?eii? ?iaioe ? aeooaeueieie, oiio ui aiie
ni?yiiaai? ia ?ic?iaeo ia/enethaaeueieo noai, aaciaaieo ia eiiooaoe?eieo
aeaiaioao oa canoinoaaiiy inoaii?o aeey iiaoaeiae ooieoe?iiaeueii?
iiaeae? ??cieo aeie?a aeaeo?iiii-ia/enethaaeueieo iaoei, nenoai oa
ia?aae.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Oaia
aeena?oaoe?eii? ?iaioe iia’ycaia c iaoeiai-oaoi?/ieie ?iaioaie, ui
aeeiioaaeeny a Ee?anueeiio oi?aa?neoao? ?iai? Oa?ana Oaa/aiea:

“Noai?aiiy oaoiieia?? i?ia?aioaaiiy aeey ia?niaeoeaieo ia?aeaeueieo
ia/enethaaeueieo eiiieaen?a”, oaia ? 97058.

“Aeine?aeaeaiiy oa oai?aoe/ia iaa?oiooaaiiy i?eioeei?a i?iaaaeaiiy ia
AII eia?ei — aeaaa?a?/ieo iiaoaeia o oi?iaeueieo oai??yo”, oaia ?97060.

“?ic?iaea eiiooaoe?eieo no?oeoo? aeey ia?aeaeueieo ia/eneaiue”, oaia
?97058.

Iaoa ?iaioe. Iaoith aeena?oaoe?eii? ?iaioe ? ?ic?iaea iaoaiaoe/ii?
iiaeae? EA oa aeine?aeaeaiiy iniiaieo ia/enethaaeueieo oa?aeoa?enoee
?aae?ciaaieo ca eiai aeiiiiiaith aeai?eoi?a iiaoaeiae aeia?eueieo
a?eoiaoe/ieo oa eia?/ieo ooieoe?e, iia?aoe?e aeiaeaaaiiy, aeiaooeo oa
ii??aiyiiy aaaauei?ic?yaeieo /enae, a oaeiae ai?iaaaeaeaiiy EA a yeino?
ia?aieea/?a aaaaoinoaiiaeo ia?aae.

Iaoiaee aeine?aeaeaiiy. Iaoaiaoe/i? iiaeae? ia/enethaaeueieo noai oa
oeeo?iaeo i?eno?i?a, iiaoaeiaaieo ia EA, iienoaaeeny ca aeiiiiiaith
oai??? a?ao?a oa aeene?aoieo ia?aoai?thaa/?a. Ei?aeoi?noue ?o
ooieoe?thaaiiy aeiaiaeeeany ca aeiiiiiaith aia?aoo /aniai? oa
iaoaiaoe/ii? eia?e, a ?ethno?aoe?y ?iaioe noai i?iaiaeeeany ca
aeiiiiiaith ae?aa?ai. Aeai?eoie iiaeaethaaiiy ?iaioe noai ia EA iienai?
iiaith i?ia?aioaaiiy N.

Iaoeiaa iiaecia ?iaioe.

— A ?iaio? aia?oa aaaaeaii iiiyooy EA, cai?iiiiiaaii eiai iaoaiaoe/io
iiaeaeue oa aeaoaeueii aeine?aeaeaii eiai ooieoe?iiaeuei? aeanoeaino?.

— Aia?oa i?e iiaoaeia? ia/enethaaeueieo oa oeeo?iaeo noai cai?iiiiiaaii
aeei?enoiaoaaoe eiiooaoe?ei? aeaiaioe cai?noue eia?/ieo.

— ?ic?iaeaii aeai?eoi ?aae?caoe?? aeia?eueii? a?eoiaoe/ii? oa eia?/ii?
ooieoe?? ca aeaa oaeoe. C aeei?enoaiiyi EA iiaoaeiaaii noaie aeiaeaaaiiy
aeaio aaaaoi?ic?yaeieo /enae ca aeaa oaeoe o noai? c e?i?eiith
e?euee?noth EA, a oaeiae noaie aeiaooeo oa ii??aiyiiy aaaaoi?ic?yaeieo
/enae ia EA.

— Cai?iiiiiaaii aeei?enoaiiy EA a ia?aieea/ao aaaaoinoaiiaeo ia?aae, ui
aea? iiaeeea?noue ?ica’ycoaaoe i?iaeaie ia?o?ooecaoe?? ye?nii iiaeie
caniaaie, ye? caaacia/othoue e?au? /ania? ioe?iee.

Oai?aoe/ia oa i?aeoe/ia oe?ii?noue ?iaioe. Aeena?oaoe?y iineoue
oai?aoeei – i?eeeaaeiee oa?aeoa?, iniiai? ?? ?acoeueoaoe ?
i??a?iaeueieie. Inoaii? aacothoueny ia aeaoaeueieo aeiaaaeaiiyo.
I?aaenoaaeai? aeine?aeaeaiiy oe?eeii iaa?oioiaothoue iniiaiee aeniiaie
i?i iiaeeea?noue aeei?enoaiiy EA a yeino? iiooaeiiai ?ino?oiaioa??th i?e
aiae?c? oa ?aae?caoe?? ia/enethaaeueieo noai.

I?aeoe/io oe?ii?noue ?iaioe aecia/athoue /ania? oa e?euee?ni?
oa?aeoa?enoeee ?aae?caoe?? aoeaaeo oa a?eoiaoeei – eia?/ieo ooieoe?e, a
oaeiae iia?aoe?e aaaaoi?ic?yaeiiai aeiaeaaaiiy, iiiaeaiiy oa ii??aiyiiy
ia iniia? EA.

Iaoa??aee aeena?oaoe?eii? ?iaioe aeei?enoiaoaaeeny i?e /eoaii?
niaoeeo?no ”Aeai?eoie ia ia?aaeao”.

Iniaenoee aianie aaoi?a a io?eiaieo ?acoeueoaoao iieyaa? a oiio, ui an?
iieiaeaiiy, ye? noaiiaeyoue nooue aeena?oaoe?eii? ?iaioe, aoee
noi?ioeueiaai? naiino?eii. O ioae?eaoe?yo, ye? iaienai? o ni?aaaoi?noa?,
caeiaoaa/aa? iaeaaeeoue:

[1], [2] – iaeyae iia?aoi??a /aniai? eia?ee, iien aeanoeainoae noai, ui
i?aoeththoue a ?aaeueiiio /an? oa ?ic?iaea cania?a aeiaaaeaiiy ??cieo
aeanoeainoae nenoai ca aeiiiiiaith aia?aoo /aniaeo eia?e.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe ?iaioe iiaeaaaeenue ia

I?aeia?iaei?e iaoeiai — oaoi?/i?e eiioa?aioe?? “No/ani? iaoiaee
oeeo?iai? ia?iaee neaiae?a a nenoaiao aei??thaaiiy, ae?aaiinoeee oa
ea?oaaiiy IN-98”, i. I?inuee;

I?aeia?iaeiiio nai?ia?? “The Information Technology Contribution to the
building of a Safe Regional Environment”, AFCEA, EUROPE, Kiev Seminar;

Nai?ia?ao eaoaae?e I? oa NAO? Ee?anueeiai oi?aa?neoaoa ?iai? Oa?ana
Oaa/aiea;

Iaoeiaeo eiioa?aioe?yo IaOEIA “Iaoea. Ethaeeia. Noni?euenoai.” o 1997 —
1999 ?ieao.

Ioae?eaoe??. Ca oaiith aeena?oaoe?? iioae?eiaaii 3 noaoo?.

No?oeoo?a oa ia’?i ?iaioe. Aeena?oaoe?y neeaaea?oueny c? anooio, o?ueio
aeaa, aeniiae?a, nieneo e?oa?aoo?e oa i?ia?ai. Caaaeueiee ia’?i ?iaioe
neeaaea? 110 noi??iie, nienie e?oa?aoo?e ia?aoiao? 89 iaeiaioaaiue.

INIIAIEE CI?NO ?IAIOE

O anooi? iieno?oueny aeooaeuei?noue ia?aii? oaiaoeee, ia?aaaae o
aeei?enoaii? EA cai?noue eia?/ieo i?e iiaoaeia? iaoaiaoe/ieo iiaeaeae
aia?aoieo cania?a aeaeo?iiii-ia/enethaaeueieo iaoei, nenoai oa ia?aae,
aea?oueny iaeyae ?iaioe oa noai i?iaeaie ia nueiaiaei?oi?e /an.

A ia?o?e aeaa? aeathoueny iniiai? iiiyooy /aniai? eia?ee [1] oa caniae
aeiaaaeaiiy aeanoeainoae noai (ei?aeoiino?, aca?iiiai aeeeth/aiiy,
aaciaee oa ?io?). Iaaiaeeoueny no?oeoo?a EA, aeine?aeaeothoueny eiai
ooieoe?iiaeuei? iiaeeeaino?. Aeey iiaoaeiae noai ia EA ?icaeyaea?oueny
iiiyooy eiiooaoe?eii? ia?aae?. Iaaaaeaii noaie aaciaeo oeeo?iaeo
i?eno?i?a (aneio?iiiee RS — o?eaa?, D — o?eaa?, noiaoi?, ia?aoai?thaa/?
eiae?a – oeo?aoi? oa aeaoeo?aoi?, ioeueoeieaeni?, e?/eeueiee) ia EA c
aeiaaaeaiiyi ei?aeoiino? ?o ?iaioe ca aeiiiiiaith /aniai? eia?ee.

A ia?aa?ao? 1.1. aeathoueny iniiai? iiiyooy /aniai? eia?ee, yea ?
iniiaiei ?ino?oiaioii aeey aeiaaaeaiiy ei?aeoiino? ?iaioe noai,
iiaoaeiaaieo ia EA.

— iiiaeeia noaiia nenoaie ui aeine?aeaeo?oueny).

A]] = » s, t I S: A(s, t).

Icia/aiiy 1.1.3. Iaoae P, Q – i?aaeeeaoe, A – aeiy. O??eea {PAQ}
iaceaa?oueny o?ieeith Oia?a, yeui ia? i?noea: P U A ® Q, oiaoi, yeui
ae?y ? A — aeiath oa P ai?ia, oiaei iiney aeeiiaiiy A — ae?? Q oaeiae
noaia a??iei.

Icia/aiiy 1.1.4. Ia/eneaiiyi (aai iiaaaeiieith) i?ia?aie (nenoaie) P
iaceaa?oueny neii/aiia aai ianeii/aiia iineiaeiaiinoue noaiia oa
ia?aoiaeia:

r0 r1 r2

s : s0 ® s1 ® s2 ®…, ui caaeiaieueiy? oaeei oiiaai:

iiioeiaeicaoeiy : s0 I S;

oniaaeeoaaiiy: «i (si+1 I ri(si));

caeii/aiiy: s — neii/aiia i caeii/o?oueny a sk, yeui sk — inoaiiie noai
a s i «r (r I T & r(sk) = 0) .

F]] = «s I SY : [[F]](s)

Icia/aiiy 1.1.6. *aniaee eiai/iee iia?aoi? ? («caaaeaee») aecia/a?oueny
ianooiiei /eiii: [[?F]](s) = » i ? 0: [[F]](s+i ). ?F — icia/a?, ui F
ia? iinoea caaaeaee: ca?ac i a iaeaooiueiio.

Icia/aiiy 1.1.7. Aiaeiioaiiyi aeinooiiinoi R(s,t) aoaeaii iaceaaoe
a?aeiioaiiy iiae noaiaie, yea icia/a? iiaeeeainoue ia?aoiaeo ?c noaio s
aei noaio t.

O?OF aai |aw|s = $t [R(s, t) & |w|t]. A?i icia/a?, ui aw aoaea ai?iei
a s, yeui w ai?ia oi/a a a iaeiiio R — aeinooiiiio noaii c s.

Icia/aiiy 1.1.9. Aaciaeie oaiii?aeueieie iia?aoeiyie iaceaathoueny:

;

;

Ia?aaeoaaiiy (Previous) A, |Aw|s = (s>0 & |w|s+1);

;

Icia/aiiy 1.1.10. Aeai oi?ioee w1 i w2 iaceaathoueny aeaiaaeaioieie (w1
= w2), yeui ia aoaeue-yeiio noaii k iiaaaeiiee s : |w1|k = |w2|k.

Icia/aiiy 1.1.11. Aeai oi?ioee w1 i w2 iaceaathoueny ii/aoeiai
aeaiaaeaioieie (w1 = Init w2), yeui: «s : |w1|0 = |w2|0.

Icia/aiiy 1.1.12. Aeiiii?aeieie /aniaeie iia?aoe?yie iaceaathoueny:

, yea icia/a?, ui ia ianooiiiio e?ioei aai caeii/eoueny ia/eneaiiy, aai
aoaea w.

, yea icia/a?, ui aai i?ioean oieueee ii/aany /ciaoiaeeoueny a
ii/aoeiaiio noaii/, aai iiia?aaeiii aoei w.

— i icia/a?, ui aai w1 aoaea caaaeaee, aai i?ney w1 aoaea w2.

— i icia/a?, ui aai caaaeaee w1, aai nii/aoeo aoei w2, a i?ney iueiai
noaei w1.

Aeey aeiaaaeaiiy oi?ioe /aniai? eia?ee aaaaeaii iiiyooy iiaeae? iiae oa
ia/eneaiiy ia i?e.

Icia/aiiy 1.1.13. Iiaeaeeth iiae iaceaa?oueny o??eea (I, a, s), aea:

I — ?ioa?i?aoaoe?y (iiaeeeai aeiaaeueia);

a — i?enai?iiy;

s — iine?aeiai?noue noai?a.

Iioa?i?aoaoeiy I niaoeeo?eo? iaeanoue ia/eneaiue, i?enaith? eiie?aoi?
aeaiaioe, ooieoe??, i?aaeeeaoe eiinoaioai, ooieoe?yi i i?aaeeeaoiei
neiaieai. I?enai?iiy a i?enaith? cia/aiiy o a?aeiia?aei?e iaeano?
eiaeii? ?iaeea?aeoaeueii? aeiaaeueii? a?eueii? ci?iii?.

w.

Icia/aiiy 1.1.15. Oi?ioea iaceaa?oueny caaeiaieueiyth/ith, yeui ?nio?
iiaeaeue, ia ye?e aiia a??ia.

?icaeyiooi aeanoeaino? /anoeiai? ei?aeoiino?, aaciaee, iiaii?
ei?aeoiino?, aa?aioiaaiino?, iaia’yceiaino?, a?aeaoeo, iino?eiino?,
?aaaoaaiiy [2].

Ia?aa?ao 1.2. i?enay/aiee iiiyooth EA – a iueiio ?icaeyaea?oueny
no?oeoo?a oa ooieoe?iioaaiiy EA. Iieacaii, ye iiaeia iienaoe ?iaioo EA
ca aeiiiiiaith /aniai? ae?aa?aie.

Icia/aiiy 1.2.1. Eiiooaoe?eiei aeaiaioii iaceaaoeiaii nenoaio (L, R, U,
D, S), aea L, R, U, D – ?ioi?iaoe?ei? iiethne, a S – ea?oth/ee iiethn.

Icia/aiiy 1.2.2. Iiethne L oa D iaceaathoueny ao?aeieie, a R oa U –
aeo?aeieie.

Oaa?aeaeaiiy 1.2.1. Ca’ycie i?ae aeo?aeieie (Out1, Out2), ao?aeieie
(In1, In2) oa ea?oth/ei (S) iiethnaie EA iiaeia iienaoe ianooiieie
aoeaaeie oi?ioeaie:

Out1 = OSUIn1 U SUIn2

Out2 = OSUIn2 U SUIn1

Oaa?aeaeaiiy 1.2.2. A oa?i?iao /aniai? eia?ee oiiao aaciaee ?iaioe EA
iiaeia iienaoe oi?ioeith:

? ((S = 1 E Out1 = In1 U Out2 = In2) U (S = 1 E Out1 = In1 U Out2 =
In2)).

A ia?aa?ao? 1.3. ?icaeyaeathoueny ooieoe?iiaeuei? aeanoeaino? EA oa
aeine?aeaeo?oueny iiaeeea?noue ?aae?caoe?? oia?ieo oa a?ia?ieo ooieoe?e
ia EA. Aaiaeeoueny iiiyooy eiiooaoe?eii? oaaeeoe?, ca aeiiiiiaith yei?
a?aenoaaeothoueny ooieoe?iiaeuei? iiaeeeaino? EA. Oai?aie 1.3.1. oa
1.3.2. ? iniiaiei ?acoeueoaoii oeueiai ia?aa?aoa.

Icia/aiiy 1.3.1. Ao?ae aoaeaii iaceaaoe ca’ycaiei, yeui eiai cao?eniaaii
a 0 /e 1, ?iaeoa – a?eueiei.

Icia/aiiy 1.3.2. Eiiooaoe?eiith oaaeeoeath aoaeaii iaceaaoe oaaeeoeth,
yea neeaaea?oueny c N noiai/ee?a. N = Bound + Nout, aea Bound –
e?euee?noue ca’ycaieo aoiae?a, Nout – e?euee?noue aeoiae?a (aeae? Nout
caaaeaee aoaea aei??aithaaoe 2). Noiai/eee, ye? aaeiia?aeathoue
ca’ycaiei aoiaeai, i?noyoue an? iiaeeea? cia/aiiy c 0 oa 1. Noiai/eee,
ye? a?aeiia?aeathoue aeoiaeai, i?noyoue ooieoe??, ye? ooai?ththoueny
i?ae ieie oa a?eueieie aoiaeaie.

Oai?aia 1.3.1. Ia iaeiiio EA iiaeia ?aae?coaaoe o?eueee iaeio oia?io
ooieoe?th – caia?a/aiiy.

Oai?aia 1.3.2. Ia iaeiiio EA iiaeia ?aae?coaaoe eeoa /ioe?e a?ia?ieo
aoeaaeo ooieoe??: aeec’thieoe?th OR, eii’thieoe?th AND, ?iie?eaoe?th E
oa iaa?iaio aioe?iie?eaoe?th I .

A ia?aa?ao? 1.4. ?icaeyaea?oueny iiaeeea?noue ooai?aiiy noai, ye?
neeaaeathoueny c aeae?eueeio EA, iaaiaeeoueny iiiyooy eiiooaoe?eii?
ia?aae?. ?icaeyaea?oueny aeai?eoi ooieoe?iioaaiiy eiiooaoe?eii? ia?aae?,
aaiaeeoueny iiiyooy oaeoo.

Icia/aiiy 1.4.1. Eiiooaoe?eiith ia?aaeath aoaeaii iaceaaoe o??eeo , aea G = G (K,E) – eiiooaoe?eiee a?ao, a yeiio K – iiiaeeia
EA, a E – iiiaeeia ca’yce?a i?ae ieie, Pol = Pol (In,Out) –iiiaeeia
ao?aeieo In oa aeo?aeieo Out iiethn?a. Ia ao?aei? iiethne In
iiaeathoueny neaiaee Sgn = {0, 1}, a ia aeo?aeieo iiethnao Out
ci?iathoueny neaiaee. Ia aeaye? iiethne aeicaiey?oueny iiaeaaaoe noae?
neaiaee, aea oe? iiethne ia aoaeaii a?aeiineoe ai? aei ao?aeieo, ai? aei
aeo?aeieo.

Icia/aiiy 1.4.2. I?ae ?iaioith eiiooaoe?eii? ia?aae? aoaeaii ?icoi?oe
io?eiaiiy neaiae?a ia aeo?aeieo iiethnao i?e iiaea/? iaaieo neaiae?a ia
ao?aei? iiethne.

Oaeei /eiii cia/aiiy neaiaeo ia aoaeue-yeiio aeo?aeiiio iiethn?
caeaaeeoue a?ae cia/aiue neaiae?a ia ao?aeieo iiethnao, oiaoi aeey
aoaeue-yei? noaie ia EA ?nio? iaaia ooieoe?iiaeueia caeaaei?noue
eiaeiiai aeoiaeo a?ae aoiae?a. Ooai?th?oueny m aoeaaeo ooieoe?e a?ae n
a?aoiaio?a, aea n = |In|, m = |Out|. A?aoiaioaie ooieoe?e ? cia/aiiy
neaiae?a ia ao?aeieo iiethnao.

Aaaeeeaith oa?aeoa?enoeeith eiiooaoe?eii? ia?aae? ? /an ?? ?iaioe aai
eiiooaoe??.

Icia/aiiy 1.4.3. Oaeoii aoaeaii iaceaaoe a?ae??cie /ano, ca yeee EA
iiaea i?eeiyoe iieiaeaiiy o a?aeiia?aeiino? c neaiaeii, yeee iaae?eoia
ia eiai ea?oth/ee ao?ae. Oiaoi /an eiiooaoe?? EA aei??aith? iaeiiio
oaeoo.

A oai?aiao 1.4.1. oa 1.4.2. i?aaenoaaeaii aea? noaie ia EA, ye?
?aae?cothoue aoeaa? ooieoe?? oo?eo Oaoa?a oa no??eeo I??na. *an ?iaioe
ia?oi? noaie neeaaea? 3 oaeoe, ae?oai? noaie – aeaa oaeoe.

A ia?aa?ao? 1.5. ca aeiiiiiaith eiiooaoe?eieo ia?aae aoaeothoueny noaie,
ye? ?aae?cothoue iniiai? aocee aeaeo?iiii-ia/enethaaeueii? oaoi?ee. Ca
aeiiiiiaith aia?aoo iaoaiaoe/ii? oa /aniai? eia?ee aeiaiaeeoueny
ei?aeoi?noue ?iaioe iaaaaeaieo noai.

Icia/aiiy 1.5.1. O?eaa?ii iaceaa?oueny i?eno??e c aeaiia no?eeeie
noaiaie ??aiiaaae, ye? i?ecia/ai? aeey caa??aaiiy ?ioi?iaoe??.

Oai?aia 1.5.1. Aneio?iiiee RS o?eaa? iiaea aooe ?aae?ciaaii ia aeaio EA.
Aaciaeo ?iaioe noaie caaacia/o? ?noeii?noue ianooiii? /aniai? oi?ioee:

(Q = 0)) U

(Q = i)), i I {0,1}.

Oai?aia 1.5.2. D — o?eaa? iiaeia ?aae?coaaoe ia o?ueio EA. Aaciaeo
?iaioe D — o?eaa?a caaacia/o? ?noeii?noue ianooiii? /aniai? oi?ioee:

(Q = i)), i I {0,1}

Oai?aia 1.5.3. Ia n EA iiaeia iiaoaeoaaoe noaie n — a?ii? aeec’thieoe??,
eii‘thieoe?? oa aeiaeaaaiiy ca iiaeoeai aeaa, i?e/iio /an ?o ?iaioe
aei??aith? aeaii oaeoai.

Oai?aia 1.5.4. Aaia?aoi? i?yiieooieo ?iioeuen?a iiaeia iiaoaeoaaoe ia
iaeiiio EA, aaciaea ?iaioe yeiai iieno?oueny oi?ioeith:

(Q = Oi)) , i I {0,1}.

Icia/aiiy 1.5.2. Eii??eith iai’yo? iaceaa?oueny i?eno??e, a yeee iiaeia
caienoaaoe oa c yeiai iiaeia /eoaoe iaeeieoeth ?ioi?iaoe??.

Oai?aia 1.5.5. Eii??eo iai’yo? iiaeia ?aae?coaaoe ia aeaio EA. sseui
/a?ac A iicia/aoe cia/aiiy, caienaia aei eii??ee, oi aaciaeo ?iaioe
noaie iiaeia iienaoe /aniaith oi?ioeith:

((K = 1 E A = D) U (K = 0 E D = A)).

Na?aae noai, ye? ?aae?cothoue ia?aoai?aiiy eiae?a, ?icaeyioo? noaie
aeaoeo?aoi?a oa oeo?aoi?a.

Icia/aiiy 1.5.3. Aeaoeo?aoi?ii iaceaa?oueny noaia, yea ia?aoai?th? eiae,
yeee iinooia? ia aoiaee a neaiae eeoa ia iaeiiio c eiai aeoiae?a.

Oai?aia 1.5.6. Aeey ?aae?caoe?? aeaoeo?aoi?a, ui ia? n aoiae?a oa 2n
aeoiae?a iaiao?aeii aeei?enoaoe 2n — 1 EA. E?euee?noue EA a noai?
e?i?eii caeaaeeoue a?ae e?eueeino? aeoiae?a aeaoeo?aoi?a.

Icia/aiiy 1.5.4. Oeo?aoi?ii aai eiaea?ii iaceaa?oueny i?eno??e, yeee
ia?aoai?th? iaeeie/iee neaiae a n ?ic?yaeiee aea?eeiaee eiae.

Oai?aia 1.5.7. Noaio oeo?aoi?a ia n aoiae?a iiaeia iiaoaeoaaoe ia EA,
i?e/iio e?euee?noue EA, aeei?enoaieo o noai?, ia a?eueoa ca n * log2n /
2. *an ?iaioe oeo?aoi?a aei??aith? aeaii oaeoai.

Icia/aiiy 1.5.5. Noiaoi?ii aoaeaii iaceaaoe noaio, yea neeaaea?oueny c n
aoiae?a oa n+1 aeoiae?a, a ooieoe?iioaaiiy yei? a?aeaoaa?oueny ianooiiei
/eiii: yeui ia ? aoiae?a iinooieoue neaiae 1 (iaia? cia/aiiy ia ye?
eiie?aoii), a ia ?ioeo aoiaeao aoaea 0, oiae? ia ?-iio aeoiae? iiaeiai
c’yaeoeny neaiae 1, a ia an?o ?ioeo aeoiaeao – 0. Cie?aia, yeui ia
aeiaeiiio ?c aoiae?a ia aoaea neaiaeo 1, oi noio aoaeaii aaaaeaoe
??aiith ioeai ? ia ioeueiaiio aeoiae? iiaeiai aooe neaiae 1.

Oai?aia 1.5.8. Noaio noiaoi?a c n aoiaeaie oa n aeoiaeaie iiaeia
?aae?coaaoe ia (n+1)*n/2 EA. *an ?iaioe noiaoi?a aei??aith? aeaii
oaeoai.

Icia/aiiy 1.5.6. Noaiith eia?/iiai ii?iao aoaeaii iaceaaoe noaio c n
aoiaeaie oa iaeiei aeoiaeii, yea i?eeia? ia aoiaee neaiaee 0 /e 1, a ia
aeoiae? aeaea? neaiae 1 eeoa a oiio aeiaaeeo, eiee e?euee?noue
iaeeie/ieo neaiae?a, ui iaae?eoea ia aoiaee, a?eueoa aai aei??aith? ca
aeayea iaia?aae caaeaia iaoo?aeueia /enei M F n. *enei M iaceaa?oueny
ii?iaiaei /eneii.

Icia/aiiy 1.5.7. Noaiith iaaei?eoa?iino? aoaeaii iaceaaoe noaio c n
aoiaeaie oa iaeiei aeoiaeii, yea i?eeia? ia aoiaee neaiaee 0 /e 1, a ia
aeoiae? aeaea? neaiae 1 eeoa a oiio aeiaaeeo, eiee e?euee?noue
iaeeie/ieo neaiae?a, ui iaae?eoea ia aoiaee, a?eueoa ca e?euee?noue
ao?aeieo ioeueiaeo neaiae?a.

Aeei?enoiaoth/e noaio noiaoi?a iiaeia io?eiaoe noaie eia?/iiai ii?iao oa
iaaei?eoa?iino?.

Oai?aia 1.5.9. Noaie eia?/iiai ii?iao oa iaaei?eoa?iino? aei??iino? n
iiaeooue aooe ?aae?ciaai? ia EA. *an ?iaioe oaeeo noai aei??aith? aeaii
oaeoai.

Icia/aiiy 1.5.8. Ioeueoeieaeni?ii iaceaa?oueny i?eno??e, yeee
ia?aoai?th? ia?aeaeuei? oeeo?ia? eiaee a iine?aeiai?.

Ioeueoeieaeni?e canoiniaothoue aeey iine?aeiaiiai iieoo caaeaii?
e?eueeino? ?ioi?iaoe?eieo neaiae?a oa ia?aaea/? ?o ia iaeei aeo?ae.

Oai?aia 1.5.10. Noaio ioeueoeieaeni?a c n aoiaeaie iiaeia ?aae?coaaoe ia
n.log2n EA. *an ?iaioe iiaoaeiaaii? noaie aei??aith? aeaii oaeoai.
Aaciaeo ?iaioe ioeueoeieaeni?a iiaeia iienaoe /aniaith oi?ioeith:

? ($! i: 1 F i F n U Out = i)

(a eiaeiee iiiaio /ano aeo?ae niieo/aii o?eueee c iaeiei aoiaeii).

Icia/aiiy 1.5.9. E?/eeueieeii iaceaa?oueny noaia, yea i?ae?aoiao?
e?euee?noue ?iioeuen?a, iiaeaieo ia ao?ae.

Oai?aia 1.5.11. Noaio e?/eeueieea c n aeoiaeaie iiaeia iiaoaeoaaoe ia
EA, i?e/iio e?euee?noue EA, caae?yieo o noai?, aei??aith? 3.n.

A ae?oa?e aeaa? oe??? ?iaioe aeine?aeaeo?oueny iiaeeea?noue iiaoaeiae
ooieoe?iiaeueii? noaie aeey ia/eneaiiy caaeaii? a?eoiaoe/ii? /e eia?/ii?
ooieoe?? ia EA. I?eaiaeyoueny aeai?eoie iiaoaeiae noaie aoeaai? ooieoe??
oa noaie aaaaoi?ic?yaeiiai aeiaeaaaiiy, iiiaeaiiy oa ii??aiyiiy.
Aeine?aeaeothoueny oaeaee?noue ?iaioe cai?iiiiiaaieo noai a caeaaeiino?
a?ae e?eueeino? EA, caae?yieo a ieo.

Ia?aa?ao 2.1. i?enay/aii aeai?eoiia? iiaoaeiae noaie ia/eneaiiy
aeia?eueii? a?eoiaoeei-eia?/ii? ooieoe?? ia EA. Neeaaei?noue iaaaaeaii?
noaie ca e?euee?noth EA ? aeniiiaioe?eiith, /an ?iaioe noaie – 2 oaeoe.

Oai?aia 2.1.1. Aeey aeia?eueii? n-a?ii? aoeaai? ooieoe?? ?nio? noaia ia
EA, yea ia/eneth? cia/aiiy oe??? ooieoe?? ca 2 oaeoe. E?euee?noue EA,
caae?yieo o noai?, ia a?eueoa ca n.2n.

Oaa?aeaeaiiy 2.1.1. sseui n-a?ia aoeaaa ooieoe?y f i?eeia? ?noeiia
cia/aiiy ia p aea?eeiaeo iaai?ao, oi e?euee?noue EA, c yeeo
neeaaea?oueny noaia ui ?aae?co? ooieoe?th f, aei??aith? p.2p.

Oaa?aeaeaiiy 2.1.2. Neeaaei?noue noaie ia EA, yea ?aae?co? aoeaao
ooieoe?th f, aeniiiaioe?eii caeaaeeoue a?ae a?iino? ooieoe?? f.

A ia?aa?ao? 2.2. aea?oueny aeai?eoi iiaoaeiae noaie noioaaiiy aeaio
aaaaoi?ic?yaeieo /enae c e?i?eiith neeaaei?noth ca e?euee?noth EA,
aeei?enoaieo a i?e.

Oai?aia 2.2.1. Aeaa aaaaoi?ic?yaeieo /enea iiaeia i?inoioaaoe ca aeaa
oaeoe.

i?, e?i?eii caeaaeeoue a?ae aei??iino? /enae.

A ia?aa?ao? 2.3. iaaaaeaii aeaa aeai?eoie iiaoaeiae noaie iiiaeaiiy
aeaio aaaaoi?ic?yaeieo /enae. Neeaaei?noue noaie, iiaoaeiaaii? ca ia?oei
aeai?eoiii (oai?aia 2.3.1.), ? aeniiiaioe?eiith, /an ?? ia/eneaiiy
aei??aith? aeaii oaeoai. Neeaaei?noue ae?oai? noaie (oai?aia 2.3.2.)
eaaae?aoe/ii caeaaeeoue a?ae ?ic?yaeiino? /enae, ye? ia?aiiiaeathoueny,
aea ?? /an ?iaioe e?i?eii caeaaeeoue a?ae ?ic?yaeiino? /enae.

Oai?aia 2.3.1. Noaio aeiaooeo aeaio aaaaoi?ic?yaeieo /enae iiaeia
?aae?coaaoe ia EA, i?e /iio e?euee?noue EA, aeei?enoaieo o noai?,
aeniiiaioe?eii caeaaeeoue a?ae ?ic?yaeiino? /enae ui ia?aiiiaeathoueny,
a /an ia/eneaiiy noaie aei??aith? aeaii oaeoai.

Oai?aia 2.3.2. Noaio aeiaooeo aeaio n — ?ic?yaeieo /enae iiaeia
?aae?coaaoe ia EA, i?e /iio e?euee?noue EA, aeei?enoaieo o noai?,
aei??aith? O(n2), a /an ia/eneaiiy noaie e?i?eii caeaaeeoue a?ae n.

A ia?aa?ao? 2.4 aea?oueny aeai?eoi iiaoaeiae noaie ii??aiyiiy aeaio
aaaaoi?ic?yaeieo /enae ia EA.

Oai?aia 2.4.1. Ia EA iiaeia iiaoaeoaaoe noaio ii??aiyiiy aeaio
aaaaoi?ic?yaeieo /enae c 2n aoiaeaie oa iaeiei aeoiaeii. Ia aoiaee
aoaeooue iiaeai? aea?eeia? caaeaiiy /enae ui ii??aiththoueny, a ia
aeoiae? aoaea iaeeieoey yeui A>B oa 0 ?iaeoa. E?euee?noue EA e?i?eii
caeaaeeoue a?ae aei??iino? /enae, ye? ii??aiththoueny.

A o?ao?e aeaa? ?icaeyaea?oueny canoinoaaiiy EA a ia?aaeao.

A ia?aa?ao? 3.1. aaiaeyoueny iniiai? iiiyooy aaaaoinoaiiaeo ia?aae.

Icia/aiiy 3.1.1. Aeaiaeieueiei a?aoii iaceaa?oueny iai???ioiaaiee a?ao
G(V1, V2, E), aea V1 oa V2 – iiiaeeie aa?oei, V1 C V2 = AE, a E –
iiiaeeia ?aaa?. Aeey eiaeiiai ?aa?a eIE, e = (v1,v2), ia? i?noea: v1IV1
oa v2IV2 aai v1IV2 oa v2IV1,.

Icia/aiiy 3.1.2. O?eaeieueiei a?aoii iaceaa?oueny a?ao G(V1, V2, V3, E1,
E2), aea Vi, i=1,3 – iiiaeeie aa?oii, a Ei, i=1,2 – iiiaeeie ?aaa?.
?aa?a c iiiaeeie Ei niieo/athoue aa?oeie, ye? c iaoiaeyoueny a iiiaeeiao
Vi oa Vi+1. I?e oeueiio aeey aoaeue-yeeo i, j , i ? j, i, j I {1, 2, 3}
ia? i?noea ??ai?noue Vi C Vj = AE.

Icia/aiiy 3.1.4. Aaaaoinoaiiaith ia?aaeath iaceaa?oueny n — aeieueiee
a?ao G = (V, E), a yeiio V={Vin, Vout, Vpr}, aea Vin – aeae?eai? n
ao?aeieo aa?oei, Vout – n aeo?aeieo aa?oei, Vpr – i?ii?aei? aa?oeie, ye?
yaeythoue niaith ia?aieea/?.

Icia/aiiy 3.1.5. k — ia?aaea/ath aeey n — ia?aae? aoaeaii iaceaaoe oaea
anoaiiaeaiiy iieiaeaiue ia?aieea/?a, ui ?nio? ca’ycie i?ae k aoiaeaie oa
k aeoiaeaie (c’?aeiaiee ao?ae oa aeo?ae aoaeaii iaceaaoe ia?ith), i?e
/iio eiaeiee aeo?ae c’yaey?oueny oi/a a a iaei?e ia??.

Icia/aiiy 3.1.6. Ia?aaea/a iaceaa?oueny iaeei aei iaeiiai (aai
iaeiicia/iith), yeui eiaeiee ao?ae c‘yaey?oueny oi/a a a iaei?e ia??.

Icia/aiiy 3.1.7. Ia?anoaiiaeith aeey n — ia?aae? aoaeaii iaceaaoe
iaeiicia/io ia?aaea/o.

Aeae? ia iniia? EA iiaeaii ?aae?caoe?th ianooiieo aaaaoinoaiiaeo ia?aae:
Aaia ia?aae?, Iiaaa ia?aae?, ia?aae? A?i?, Eein ia?aae? oa ia?aae?
iaoaeeea.

A ia?aa?ao? 3.2. ?icaeyaeathoueny iaoiaee ia?aaea/? aeaieo oa
aeine?aeaeothoueny aeai?eoie ia?o?ooecaoe?? ia iaaaaeaieo a ia?aa?ao?
3.1. oiiieia?yo aaaaoinoaiiaeo ia?aae.

A ia?aa?ao? 3.2.1. ?icaeyaea?oueny caaea/a ia?o?ooecaoe?? ia ia?aae?
A?i?. Aea?oueny aeai?eoi iiaoaeiae noaie, yea iiaea ?aae?coaaoe
aeia?eueio, iaia?aae caaeaio ia?anoaiiaeo.

Oai?aia 3.2.1. Aeia?eueio ia?anoaiiaeo iiaeia ?aae?coaaoe ia ia?aae?
A?i?.

Ia?aa?ao 3.2.2. i?enay/aii iiaeeeaino? ?aae?caoe?? Aaia ia?aae? ia EA.
Aeai?eoie iiaoaeiae noai ia?aieea/?a Aaia ia?aae? aeathoueny a
aeiaaaeaii? oai?aie 3.2.2.1.. A oai?ai? 3.2.2.2 aea?oueny oi?ioea
ciaoiaeaeaiiy e?eueeino? an?o iiaeeeaeo oeyo?a a?ae caaeaieo aoiaeo aei
aeoiaeo, iaaiaeeoueny aeai?eoi ?o ciaoiaeaeaiiy.

Oai?aia 3.2.2.1. Ia?aieea/? Aaia ia?aae?, a ioaea ? any Aaia ia?aaea,
iiaeooue aooe ?aae?ciaai? ia EA.

Oai?aia 3.2.2.2. An? iiaeeea? oeyoe a Aaiia ?ici??o n ia?aae? a?ae
aoiaeo X aei aeoiaeo Y aecia/athoueny ??cieoeath S = (Y — X) mod 2n, i?e
/iio ?o e?euee?noue Rn aecia/a?oueny oi?ioeith:

Rn =

Iaaiaeeoueny i?eeeaae ciaoiaeaeaiiy an?o oeyo?a o Aaia ia?aae?.
Ciaeaeai? oeyoe iiaeathoueny o aeaeyae? aea?aaa ia?o?ooecaoe??.

A ia?aa?ao? 3.2.3 ?icaeyaeathoueny aeai?eoie ia?aaea/? aeaieo ia Iiaaa
ia?aae?. Ii??aiththoueny /ania? ioe?iee aeai?eoi?a ia?o?ooecaoe?? aeey
Iiaaa ia?aae?, iiaoaeiaaii? ia cae/aeieo ia?aieea/ao oa ia EA.

Oai?aia 3.2.3.1. Ia?aaea/a aeaieo ?c aoiaeo S aei aeoiaeo D ia iiaaa
ia?aae? ?ici??o n, iiaoaeiaaii? ia cae/aeieo ia?aieea/ao, a?aeaoaa?oueny
ca log2n oaeo?a.

Oai?aia 3.2.3.2. Ia?aaea/a aeaieo ?c aoiaeo S aei aeoiaeo D ia Iiaaa
ia?aae? ?ici??o n, iiaoaeiaaii? ia EA, a?aeaoaa?oueny ca 2 oaeoe.

Icia/aiiy 3.2.3.1. Aeaa iia?aeiieaiiy iaceaathoueny eiioe?eoieie, yeui
aiie iathoue ni?eueia a?eii Wi, oiaoi aiie iiaeii? i?ieoe ii iaeiiio
eaiaeo i-ei oa i+1 — ei noaiaie.

Icia/aiiy 3.2.3.2. Iiiaeeio iia?aeiieaiue aoaeaii iaceaaoe
iaeiioe?eooth/ith, yeui aeiaei? aeaa iia?aeiieaiiy c oe??? iiiaeeie ia
eiioe?eoothoue i?ae niaith.

Oai?aia 3.2.3.3. Iiiaeeia c m iia?aeiieaiue iiaea aooe ?icaeoa ia
iaeiioe?eooth/? iiiaeeie, i?e/iio e?euee?noue inoaii?o ia iaioa i?ae m /
log2n, aea n – ?ici?? ia?aae? (o aeiaaeeo iiaii? caaaioaaeaiino?
ia?aae?) oa ia a?eueoa i?ae m (yeui eiaeia iia?aeiieaiiy eiioe?eoo? c
eiaeiei). Inoaii?e aeiaaeie iiaeeeaee, iai?eeeaae, yeui o?aaa ia?aaeaoe
m iaeiaeiaeo iia?aeiieaiue.

Oai?aia 3.2.3.4. sseui ia Iiaaa ia?aae? ?ici??o n, iiaoaeiaaii? ia EA,
iiaeia ia?aaeaoe m iia?aeiieaiue ca T oaeo?a, oi m / log2n F T F m.

Ni?ooth/ei ia?aaeai i?eae?ey?oueny aaaaoi oaaae caaaeyee ?o iioe?aiiio
aeei?enoaiith a ??cieo aaeocyo. Aiie canoiniaothoueny i?e iiaoaeia?
nenoai ia?aeaeueii? ia?iaee ?ioi?iaoe??, noai aeinooio aei aioo??oi?o oa
ciai?oi?o i?eno?i?a. sse i?aaeei, ni?ooth/? ia?aae? aoaeothoueny c
eiiia?aoi??a. Caaaeyee oiio, ui eiiia?aoi?e aoaeue-yei? neeaaeiino?
iiaeooue aooe iiaoaeiaai? ia EA, inoaii? iiaeia aeei?enoiaoaaoe i?e
iiaoaeia? ni?ooth/eo ia?aae. A ianooii?e /anoei? aeaae iieno?oueny
iiaoaeiaa ni?ooth/eo ia?aae.

A ia?aa?ao? 3.3. aeine?aeaeo?oueny iiaoaeiaa ni?ooth/eo ia?aae ia EA.

Icia/aiiy 3.3.1. Eiiia?aoi?ii aoaeaii iaceaaoe noaio ii??aiyiiy aeaio
/enae.

Oaa?aeaeaiiy 3.3.1. n — ?ic?yaeiee eiiia?aoi? iiaeia ?aae?coaaoe ia EA,
e?euee?noue yeeo e?i?eii caeaaeeoue a?ae n. *an ?iaioe n — ?ic?yaeiiai
eiiia?aoi?a e?i?eii caeaaeeoue a?ae n.

Oaa?aeaeaiiy 3.3.2. Noaia ceeooy aeaio a?aeni?oiaaieo iine?aeiaiinoae
iiaea aooe iiaoaeiaaia ia EA.

Oaa?aeaeaiiy 3.3.3. Ni?ooth/a ia?aaea Aao/a?a iiaea aooe iiaoaeiaaia ia
EA.

A aeiaeaoeo 1 iaaiaeeoueny i?ia?aia iiaeaethaaiiy eiiooaoe?eii? ia?aae?.

A aeiaeaoeo 2 iaaiaeeoueny i?ia?aia iiaeaethaaiiy ia?aaea/? aeaieo ia
Iiaaa oa Aaia ia?aaeao.

INIIAI? ?ACOEUeOAOE ?IAIOE

Iniiaieie ?acoeueoaoaie aeena?oaoe?eii? ?iaioe ? noai?aiiy iaoaiaoe/ii?
iiaeae? EA, aeine?aeaeaiiy ?iaioe eiiooaoe?eieo ia?aae oa cai?iiiioaaiiy
aeai?eoi?a ?aae?caoe?? iniiaieo ia/enethaaeueieo noai oeeo?iai? oaoi?ee
ia EA. Ia iniia? EA:

Iiaoaeiaaii ooieoe?iiaeuei? noaie oeeo?iaeo i?eno?i?a.

Iaaaaeaii aeai?eoi iiaoaeiae eiiooaoe?eii? noaie, yea ?aae?co?
aeia?eueio iaia?aae caaeaio aoeaao ooieoe?th, /an ia/eneaiiy yei?
neeaaea? aeaa oaeoe.

Iiaoaeiaaii eiiooaoe?ei? noaie aeiaeaaaiiy, iiiaeaiiy oa ii??aiyiiy
aeaio aaaaoi?ic?yaeieo /enae c ??cieie e?euee?nieie oa /aniaeie
oa?aeoa?enoeeaie.

Cai?iiiiiaaii aeei?enoaiiy oa ?aae?caoe?th ia?aieea/?a aaaaoinoaiiaeo
?iciiae?eaieo ia?aae ia eiiooaoe?eieo aeaiaioao.

Iniiaiee ci?no aeena?oaoe?? iioae?eiaaii a ianooiieo i?aoeyo:

1. Aeeaiaaoeue I.I., Iaaeaaae?a I.A. Iien neeaaeieo nenoai ?ioi?iaoe??
ca aeiiiiiaith /aniaeo eia?e // A?niee Ee?anueeiai oi?aa?neoaoo, Na??y
o?c.-iao. iaoe, Aeione ?2, Ee?a, 1996 ?., noi?. 106-114.

2. Aeeaiaaoeue I.I., Iaaeaaae?a I.A. Aeei?enoaiiy aia?aoo /aniaeo eia?e
aeey aeine?aeaeaiiy iniiaieo aeanoeainoae i?ia?ai // A?niee Ee?anueeiai
oi?aa?neoaoo, Na??y o?c.-iao. iaoe, Aeione ?1, Ee?a, 1996 ?., noi?.
187-191.

3. Iaaeaaae?a I.A. Aca?iia aeeeth/aiiy // A?niee Ee?anueeiai
oi?aa?neoaoo, Na??y o?c.-iao. iaoe, Aeione ?2, Ee?a, 1998 ?.,
noi?.214-221.

Iaaeaaae?a I.A. Aeine?aeaeaiiy oa ?ic?iaea ia/enethaaeueieo noai,
aaciaaieo ia eiiooaoe?eieo aeaiaioao. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.03 — iaoaiaoe/ia oa
i?ia?aiia caaacia/aiiy ia/enethaaeueieo iaoei oa nenoai. — Ee?anueeee
oi?aa?neoao ?iai? Oa?ana Oaa/aiea, Ee?a, 1999.

Aeena?oaoe?y i???ioiaaia ia aeine?aeaeaiiy oa ?ic?iaeo ia/enethaaeueieo
noai, aaciaaieo ia eiiooaoe?eieo aeaiaioao (EA) oa ia ?o canoinoaaiiy
i?e ?ic?iaoe? ooieoe?iiaeueieo iiaeaeae aia?aoieo noai. A aeena?oaoe??
aaiaeeoueny iiiyooy eiiooaoe?eiiai aeaiaioa, aeine?aeaeothoueny eiai
ooieoe?iiaeuei? aeanoeaino?, aeiaiaeyoueny ia?aaaae aeei?enoaiiy EA
cai?noue eia?/ieo aeaiaio?a i?e ?ic?iaoe? oeeo?iaeo noai. Cai?iiiiiaaii
aeai?eoi iiaoaeiae ia/enethaaeueii? noaie ia EA, yea ?aae?co? aeia?eueio
a?eoiaoe/io /e eia?/io ooieoe?th. Aeine?aeaeaii ?iaioo noai
aaaaoi?ic?yaeiiai aeiaeaaaiiy, iiiaeaiiy oa ii??aiyiiy ia EA.
Iaaiaeeoueny aeei?enoaiiy EA i?e iiaoaeia? aaaaoinoaiiaeo ia?aae oa
?ica’yceo caaea/ ia?o?ooecaoe??.

Eeth/ia? neiaa: eiiooaoe?eiee aeaiaio, a?eoiaoe/i? oa eia?/i? noaie,
aaaaoinoaiia? ia?aae?, ni?ooth/? ia?aae?.

Iaaeaaaeaa I.A. Enneaaeiaaiea e ?ac?aaioea au/eneeoaeueiuo noai,
aace?othueony ia eiiiooaoeeiiiuo yeaiaioao. — ?oeiienue.

Aeenna?oaoeey ia i?eia?aoaiea iao/iie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.05.03 — iaoaiaoe/aneia
e i?ia?aiiiia iaania/aiea au/eneeoaeueiuo iaoei e nenoai. — Eeaaneee
oieaa?neoao eiaie Oa?ana Oaa/aiea, Eeaa, 1999.

ai iiiai?ac?yaeiiai neiaeaiey, oiiiaeaiey e n?aaiaiey ia EY. I?eaiaeeony
eniieueciaaiea EY i?e iino?iaiee naoae ni iiiaeie ninoiyieyie e ?aoaiee
caaea/ ia?o?ooecaoeee.

Aeenna?oaoeey ninoieo ec 7 ?acaeaeia: anooieaiey, o?ao aeaa
(ia?aa?aoia), caeeth/aiey, nienea eeoa?aoo?u e aeiiieiaiey.

Ai anooieaiee ?anniao?eaaaony nia?aiaiiia ninoiyiea ?acaeoey iao/iuo
aeinoeaeaiee a iaeanoe ?ac?aaioee noai oeeo?iauo ono?ienoa, a?oeoaeoo?
YAI e oiiieiaee naoae, aeai?eoiia ia?o?ooecaoeee, aa?eoeeaoeee.

A ia?aa?aoa 1.1 aaiaeeony iiiyoea eiiiooaoeeiiiiai yeaiaioa (aeaeaa –
EY) ia ooieoeeiiaeueiii o?iaia, ?anniao?eaaaony aai no?oeoo?a, i?aaeea
eiiiooaoeee e ia?aaea/e neaiaeia. Aeathony iniiaiua ii?aaeaeaiey e
aaiaeyony iniiaiua iiiyoey. Iino?iaiu aoeaau oi?ioeu, iienuaathuea
?aaioo EY e i?eaaaeaiu eo oaaeeoeu enoeiiinoe.

Ia?aa?ao 1.2 enneaaeoao ooieoeeiiaeueiua aiciiaeiinoe EY. No?iyony ana
aiciiaeiua oia?iua e aeia?iua aoeaau ooieoeee, eioi?ua iiaoo auoue
?aaeeciaaiu ia iaeiii EY.

A ia?aa?aoa 1.3. aaiaeeony iiiyoea eiiiooaoeeiiiie naoe.
?anniao?eaathony aiciiaeiinoe niaaeeiaiey ?aciuo EY aeey ia?aciaaiey
neiaeiuo noai. I?e iiiiue iaoaiaoe/aneie eiaeee enneaaeoaony ?aaioa
eiiiooaoeeiiiuo naoae.

A ia?aa?aoa 1.4. i?aaenoaaeaiu noaiu iniiaiuo oeeo?iauo ono?ienoa ia EY
n aeieacaoaeuenoaii ei??aeoiinoe eo ?aaiou.

Ai aoi?ie aeaaa yoie ?aaiou enneaaeoaony aiciiaeiinoue iino?iaiey
aiia?aoiie noaiu caaeaiiie a?eoiaoe/aneie eee eiae/aneie ooieoeee.

A ia?aa?aoa 2.1. aeaaony aeai?eoi iino?iaiey noaiu aeey i?iecaieueiie
aoeaaie ooieoeee. Ianiio?y ia oi, /oi nei?inoue aa ?aaiou ninoaaeyao
anaai aeaa oaeoa, eiee/anoai caaeaenoaiaaiiuo a noaia EY
yeniiiaioeeaeueii caaeneo io eiee/anoaa a?aoiaioia.

Iniiaiui ?acoeueoaoii ia?aa?aoa 2.2. yaeyaony iino?iaiea noaiu
noiie?iaaiey aeaoo iiiai?ac?yaeiuo /enae, neeaaeuaathuay /enea ca aeaa
oaeoa.

A ia?aa?aoa 2.3. ?anniao?eaaaony aeaa aeai?eoia oiiiaeaiey
iiiai?ac?yaeiuo /enae ia EY. Ia?aue aeai?eoi eiaao yeniiiaioeeaeueioth
neiaeiinoue i?e nei?inoe ?aaiou aeaa oaeoa, aoi?ie – eaaae?aoe/ioth
neiaeiinoue i?e eeiaeiie a?aiaiiie ioeaiea.

Ia?aa?ao 2.4. iienuaaao noaio n?aaiaiey iiiai?ac?yaeiuo /enae, eioi?ay a
aeaeueiaeoai aoaeao eniieueciaaoueny i?e iino?iaiee eiiia?aoi?ia a
ni?oe?othueo naoyo.

A o?aoueae aeaaa ?anniao?eaaaony oiio?aaeaiea EY a naoyo. *anoi iaeei
i?ioeanni? niaaeeiyaony n ianeieueeeie ae?oaeie, a i?e ia?aaea/a
eioi?iaoeee iaiaoiaeeii aua?aoue oio iooue, eioi?ue aaaeao e ?aoaieth
caaea/e. Eae i?aaeei, ia?aaeaaaaiua aeaiiua niaea?aeaony a iaeioi?ii
?aaeno?a (eee iiiaeanoaa ?aaeno?ia – iaiyoe). I?e iiiiue eiiiooaoeeiiiuo
iaoaieciia ia?o?ooecaoi?a i?ienoiaeeo niaaeeiaiea auoiaeia ?aaeno?a
iaeiiai i?ioeanni?iiai yeaiaioa (IY) ni aoiaeaie ?aaeno?a ae?oaiai IY
oeiie. Iu iieaaeai, /oi eiiiooaoeeiiiua iaoaieciu niaaeeiaiey iaeiiai IY
n ae?oaei iiaeii ?aaeeciaaoue ia EY aeey i?iecaieueiie oiiieiaee. N
?inoii noaiaie oiiieiaee naoe aic?anoaao e neiaeiinoue eiiiooaoeeiiiuo
noai.

A ia?aa?aoa 3.1 ?anniao?eaathony naoae ni iiiaeie ninoiyieyie e eo
iniiaiua eiiiooaoeeiiiua iaoaieciu n ?aaeecaoeeae iineaaeieo ia EY.

A ia?aa?aoa 3.2 enneaaeothony i?iaeaiu ia?o?ooecaoeee a naoyo.
?anniao?eaaaony iniiaiay caaea/a ia?o?ooecaoeee – ia?aaea/a iaeaoa
aeaiiuo io iaeiiai e ae?oaiio IY, iienaiu aeai?eoiu ia?aaea/e
eioi?iaoeee ia ?aciuo oiiieiaeyo e oeacaiu i?aaeea eiiiooaoeee.

A ia?aa?aoa 3.3. iienuaaaony iauee iiaeoiae e iino?iaieth noai
ni?oe?othueo naoae, iniiaie eioi?uo yaeyaony EY.

Iniiaiuie ?acoeueoaoaie aeenna?oaoeeiiiie ?aaiou yaeyaony nicaeaiea
iaoaiaoe/aneie iiaeaee EY, enneaaeiaaiea ?aaiou eiiiooaoeeiiiuo naoae e
i?aaenoaaeaiea aeai?eoiia ?aaeecaoeee iniiaiuo au/eneeoaeueiuo noai
oeeo?iaie oaoieee ia EY. Ia iniiaa EY:

Iino?iaii ooieoeeiiaeueiua noaiu oeeo?iauo ono?ienoa.

I?aaenoaaeai aeai?eoi iino?iaiey eiiiooaoeeiiiie noaiu, eioi?ay
?aaeecoao ethaoth caaeaiioth aoeaao ooieoeeth, a?aiy au/eneaiey eioi?ie
?aaii aeaoi oaeoai.

Iino?iaiu eiiiooaoeeiiiua noaiu neiaeaiey, oiiiaeaiey e n?aaiaiey aeaoo
iiiai?ac?yaeiuo /enae n ?aciuie eiee/anoaaiiuie e a?aiaiiuie
oa?aeoa?enoeeaie.

I?aaeeiaeaii eniieueciaaiea e ?aaeecaoeeth ia?aeeth/aoaeae naoae ni
iiiaeie ninoiyieyie.

Eeth/aaua neiaa: eiiiooaoeeiiiue yeaiaio, a?eoiaoe/aneea e eiae/aneea
noaiu, naoe ni iiiaeie ninoiyieyie, ni?oe?othuea naoe.

Medvedev M.G. Investigation and development of calculation circuits
using commutation elements. — Manuscript.

Thesis for the Degree of Candidate of Physics-Mathematical Science in
Speciality 01.05.03 — Computer Software. — Taras Shevchenko Kyiv
University, Kyiv, 1999.

The thesis is devoted to investigation and design of computing schemes,
based on commutation element (CE), its usage in functional models
development for hardware. The idea of CE, its functional properties, the
advantages of using CE instead of logic elements in hardware circuits
design are dealt within the thesis. The algorithm for arithmetic or
logic function realization is proposed, based on CE. Polydigital
addition, multiplication and comparation schemes are considered. A great
attention is paid to the CE usage in multistage interconnection networks
construction and routing tasks solution.

Keywords: commutation element, arithmetic and logic schemes, multistage
interconnection networks, sorting networks.

Aeooeia A.I. Neioac oeeo?iauo aaoiiaoia, I. Oeciaoaec , 1962, 216n.

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{

Rn-1(S/2), yeui S ia?ia

Rn-1((S-1)/2) + Rn-1((S+1)/2), yeui S iaia?ia

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