3

Iaoe?iiaeueia aaaionoai c ieoaiue ?ioi?iaoecaoe??

i?e I?aceaeaioia? Oe?a?ie

Aea?aeaaiee iaoeiai-aeine?aeiee ?inoeooo

?ioi?iaoe?eii? ?io?ano?oeoo?e

CA?A?II Aeieo?i Aeieo?iae/

OAeE 681.513

IA?AEAEUeI? A?EOIAOE*I? IA*ENEAIIss

IA EE?OEIIEO AAOIIAOAO

05.13.06 — Aaoiiaoeciaai? nenoaie oi?aae?iiy

oa i?ia?aneai? ?ioi?iaoe?ei? oaoiieia??

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Euea?a-1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Aea?aeaaiiio oi?aa?neoao? «Euea?anueea iie?oaoi?ea»

I?i?noa?noaa ina?oe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,

Aaeueeianueeee Aieiaeeie? Ieaenaiae?iae/,

caa?aeoth/ee a?aeae?eii Aea?aeaaiiai iaoeiai-aeine?aeiiai ?inoeoooo
?ioi?iaoe?eii? ?io?a-no?oeoo?e

Io?oe?ei? iiiiaioe: aeieoi? oaoi?/ieo iaoe, noa?oee iaoeiaee ni?a?.

?onei Aiaaeai Iaaeiae/,

caa?aeoth/ee a?aeae?eii O?ceei-iaoai?/iiai ?inoeoooo ?i. A.A.Ea?iaiea
IAI Oe?a?ie

eaiaeeaeao oaoi?/ieo iaoe

Iiioye TH??e Aieiaeeie?iae/,

noa?oee iaoeiaee ni?a?ia?oiee Aea?aeaaiiai iaoeiai-aeine?aeiiai
?inoeoooo ?ioi?iaoe?eii? ?io?ano?oeoo?e

I?ia?aeia onoaiiaa: ?inoeooo e?aa?iaoeee ?i. A.I.Aeooeiaa IAI

Oe?a?ie, a?aeae?e ea?oth/eo iaoei ? nenoai, i. Ee?a.

Caoeno a?aeaoaeaoueny «15»_eeiiy_ 1999 ?ieo i 16 aiae. ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.813.01 a Aea?aeaaiiio
iaoeiai-aeine?aeiiio ?inoeooo? ?ioi?iaoe?eii? ?io?ano?oeoo?e (290601,
i.Euea?a, aoe. Iaoeiaa, 5a).

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Aea?aeaaiiai
iaoeiai-aeine?aeiiai ?inoeoooo ?ioi?iaoe?eii? ?io?ano?oeoo?e (290601,
i.Euea?a, aoe.Iaoeiaa,5a).

Aaoi?aoa?ao ?ic?neaiee «14»o?aaiy1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

aeieoi? oaoi?/ieo iaoe, no.iaoe.ni._________________ Aoiue ?.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue i?iaeaie. A aeaiee /an iai?oeeeny o?e iniiai?
oaiaeaioe?? ?icaeoeo ia/enethaaeueii? oaoi?ee. Oea i?aeaeuaiiy
ia/enethaaeueii? iiooaeiino?; cieaeaiiy nia?aa?oino? a?oo ?ioi?iaoe??;
iaaeeaeaiiy aei ei?enooaa/a aai aei i?eeaae?a oa i?ioean?a, ye?
aeei?enoiaothoue ?ioi?iaoe?th. Aeaia aeena?oaoe?eia ?iaioa ia?
a?aeiioaiiy aei ia?oeo aeaio oaiaeaioe?e.

A?eueo?noue no/anieo eiii’thoa??a no?oeoo?ii ?icae?eai? ia aeoeaiee
aeaiaio — oeaio?aeueiee i?ioeani? ? ianeaio iai’youe. Oiio, i?e
ca?eueoaii? ia’?io iai’yo? aeei?enoaiiy eiaeiiai ?? a?oo ciaioo?oueny. C
oeueiai aeieeaa?, ui i?aeaeuaiiy ia/enethaaeueii? iiooaeiino? aeey
caaea/ c aaeeeeie ia’?iaie aeaieo a cia/i?e i??? iia’ycaia c ?icaeoeii
iaoiae?a ?icia?aeaethaaiiy ia/eneaiue.

Iania? ia?aeaeuei? ia/eneaiiy noathoue ana a?eueo iaiao?aeieie aeey
noai?aiiy oa aiae?co iiaeaeae neeaaeieo nenoai, a oaeiae aeey ia?iaee
neaiae?a ? ia’?iieo cia?aaeaiue. Oaeiae iio??aieie ? iiaeae? i?eno?i?a
oa aeai?eoie, ye? aeicaieyoue aeaoaai oa i?inoi aeeiioaaoe
ianiai-ia?aeaeuei? ia/eneaiiy. Ciaioaiiy nia?aa?oino? ia an?o noaae?yo
i?iaeooaaiiy oa ae?iaieoeoaa ca ?aooiie aenieiai nooiaiy
noaiaea?oecaoe?? oa iaeiioeiiino? ? iiaeeeaei, yeui aaea?oueny ?icaeoe
noaio ia iaeiaeia? o?aaiaioe, ca’ycee i?ae yeeie iiaoi?ththoueny i?e
ia?aoiae? a?ae iaeiiai o?aaiaioo aei ?ioiai. Aeanoea?noue ?aaoey?iino?
no?oeoo?e i?eoaiaiia iiaeae? ee?oeiieo aaoiiao?a, yea na?aae ?ioeo
iiaeaeae iaeii??aeieo nenoai oa?aeoa?eco?oueny oei, ui a i?e a?aenooi?
caniae eiiooaoe?? i?ae aeaiaioaie. Oea aea? iiaeeea?noue ni?inoeoe ??
aia?aoio ?aae?caoe?th ? iaoiaee neioaco i?ia?ai.

Aiae?c ioae?eaoe?e i?aeoaa?aeea, ui iaia? iaoaiaoe/ii? iiaeae?
ee?oeiiiai aaoiiaoa aeey aeeiiaiiy an?o a?eoiaoe/ieo iia?aoe?e oa
ae?ac?a. Noai?aiiy oaei? iiaeae? noaei a iiooiaoii aei ?icaeoeo
oe?ieiai eeano iiaeaeae noioanoe/iiai ia?aeae?cio i?e ia?iaoe?
?ioi?iaoe??, ine?eueee a?eoiaoeei-eia?/i? iia?aoe?? ? aaciaeie. Oaeei
/eiii, aeine?aeaeaiiy aeaiaioa?ieo iaeii??aeieo ia/enethaaeueieo
no?oeoo?, cie?aia no?oeoo? aac cania?a eiiooaoe?? i?ae aeaiaioaie — oae
caaieo ee?oeiieo aaoiiao?a, aeioe?euei? ye c oai?aoe/ii?, oae ? c
i?aeoe/ii? oi/ie ci?o.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa
aeeiioaaeany a ?aieao caaaeaiiy Aea?aeaaii? iaoeiai-oaoi?/ii? i?ia?aie
“Ia?niaeoeai? caniae ia/enethaaeueii? oaoi?ee. Aiae?oe/ia
i?eeaaeiaoaeoaaiiy. Oaeaeiioi?eaoe??.” I?i?noa?noaa Oe?a?ie o ni?aaao
iaoee ? oaoiieia?e, yea aeeiio?oueny a Aea?aeaaiiio oi?aa?neoao?
“Euea?anueea iie?oaoi?ea”.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith ?iaioe ? aeine?aeaeaiiy
iiaeeeaino? canoinoaaiiy ee?oeiieo aaoiiao?a aeey ?aae?caoe??
ia?aeaeueieo a?eoiaoe/ieo oa eia?/ieo ia/eneaiue. Aeey ?? aeinyaiaiiy
aoee iinoaaeai? ianooii? caaea/?.

· ?ic?iaeoe iiaeaeue ee?oeiiiai aaoiiaoa, ui iiaea aooe aeei?enoaia aeey
iiaoaeiae ia?aeaeueieo i?eno?i?a oa i?ia?ai, a iniiao yeeo iieeaaeaii
aeai?eoie ?icia?aeaethaaiiy eia?/ieo oa a?eoiaoe/ieo iia?aoe?e ia ??ai?
ie?aieo a?o?a aeaieo.

· Aeine?aeeoe ? ii??aiyoe ??ci? nenoaie i?aaee ooieoe?iioaaiiy oaeeo
iiaeaeae a eeane/i?e ? ciaeici?ii?e nenoai? eiaeoaaiiy /enae, aecia/eoe
aeaaa?a?/i? aeanoeaino? i?aaee.

· Aecia/eoe iioeiaeueio nenoaio eiaeoaaiiy oa nenoaio i?aaee
ooieoe?iioaaiiy ee?oeiiiai aaoiiaoa aeey aeeiiaiiy ia?aeaeueieo
a?eoiaoe/ieo ia/eneaiue ca ianooiieie e?eoa??yie iioeiaeueiino?: a)
i?i?iaeueia e?euee?noue i?aaee; a) iaeneiaeueia oaeaee?noue aeinyaiaiiy
?acoeueoaoo; a) ooieoe?iiaeueia iiaiioa a eean? /ioe?ueio a?eoiaoe/ieo
iia?aoe?e — aeiaeaaaiiy, a?aei?iaiiy, iiiaeaiiy oa ae?eaiiy.

· ?ic?iaeoe oa iaa?oiooaaoe aeai?eoie ?aae?caoe?? eia?/ieo oa
a?eoiaoe/ieo iia?aoe?e iaae ae?enieie oa eiiieaenieie /eneaie.

· Noai?eoe aaoiiaoeciaaio nenoaio aeey ?i?oaoe?eiiai iiaeaethaaiiy
ee?oeiieeo aaoiiao?a c aeia?eueiith nenoaiith i?aaee.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. A aeena?oaoe?ei?e ?iaio?
aia?oa ?ic?iaeaii oai??th iiaoaeiae ee?oeiiiai aaoiiaoa aeey aeeiiaiiy
ia?aeaeueieo ia/eneaiue c ae?enieie oa eiiieaenieie /eneaie oa aaeoi?aie
ia ??ai? ie?aieo a?o aeaieo, a naia:

· aaaaeaii iiao iiaeaeue ee?oeiiiai aaoiiaoa aeey a?eoiaoe/ieo
ia/eneaiue c ae?enieie oa eiiieaenieie /eneaie;

· aia?oa aeei?enoaii iaaaa?ia?io nenoaio eiaeoaaiiy ae?enieo oa
eiiieaenieo /enae aeey ee?oeiieo aaoiiao?a;

· cai?iiiiiaaii iiaee iaoiae aneio?iiieo iia?oieo ia/eneaiue ae?enieo oa
eiiieanieo ae?ac?a;

· aia?oa ?icaeyiooi nenoaio i?aaee ee?oeiiiai aaoiiaoa aeey ?iaioe i?e
iayaiino? aeaoaeoieo eii??ie;

· ?icaeyiooi iia? ee?oeii? aeai?eoie aeey ia?aoai?aiiy /enae c
aea?eeiai? nenoaie i?aaenoaaeaiiy a iaaaa?ia?io;

· aia?oa ?icaeyiooi i?aaeea aea?aaeaioiiai ia?aoai?aiiy aaoiiaoiiai
i?inoi?o ia aeiaaeie eiio?ioaeueiino? noaio eiaeii? eii??ee;

· ciaeaeaii i?eioeeie iiaoaeiae aaoiiaoeciaaii? nenoaie aeey
?i?oaoe?eiiai iiaeaethaaiiy ee?oeiieo aaoiiao?a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Oai??y, iaoiaee, aeai?eoie
? i?ia?aie, ye? aoee ?ic?iaeai? a aeena?oaoe?ei?e ?iaio?, aeicaieythoue:

· i?iaeooaaoe aeaoaa? i?eno?i? c iaeii??aeiith no?oeoo?ith o aeaeyae?
caeaoieo aei ia?aiaeaoooaaiiy i?e?inoai “ia?iaeyth/i? iai’yo?” aeey
aeeiiaiiy ianiaeo ia?aeaeueieo ia/eneaiue a aeayeiio eean? caaea/;

· i?aeaeuoaaoe iaae?ei?noue aeacaieo i?eno?i?a ca ?aooiie ?o
i?aoeacaeaoiino? i?e aeieeiaii? aeaoaeoieo eii??ie;

· canoiniaoaaoe oa a?aeeaaiaeaeoaaoe aneio?iii? aeai?eoie ia?iaee
?ioi?iaoe??, ye? iiaeooue aooe ?aae?ciaai? aeacaieie i?eno?iyie;

· iiaeaethaaoe oa i?iaiicoaaoe o?ae ?icaeoeo ??cieo i?ioean?a, ye?
i?aaenoaaeythoueny aneio?iiieie i?aaeeaie i?aenoaiiaee noai?a, cie?aia,
i?ioean?a aneio?iiieo a?eoiaoe/ieo ia/eneaiue.

Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe. ?acoeueoaoe ?iaioe aoee aeei?enoai?
oa ai?iaaaeaeai? a ianooiieo i?aai?caoe?yo: Euea?anuee? i?nuee?
aeaeo?e/i? ia?aae? — aeai?eoi ianooaaoaaiiy aeaeo?e/ieo noai ?c
caa?aaeaiiyi iaaeien?a oa iicia/aiue; ?inoeooo i?eeeaaeieo i?iaeai
iaoai?ee ? iaoaiaoeee ?i. ss.N.I?aeno?eaa/a IAI Oe?a?ie, i. Euea?a —
aenia?aiaioaeueia ioe?iea i?aaeeueiino? aneio?iiieo aeai?eoi?a;
Ea?iaonueea a?aeae?eaiiy ?inoeoooo aaio?ceee ?i. N.?.Noaaio?ia IAI
Oe?a?ie, i. Euea?a — ee?oeiia iiaeaeue ?iciianthaeaeaiiy naeaaiai
iioieo; A?ei?onueeee aea?aeaaiee oi?aa?neoao, i. I?inuee —
ai?iaaaeaeaiiy a iaa/aeueiee i?ioean ia oaeoeueoao? i?eeeaaeii?
iaoaiaoeee oa ?ioi?iaoeee; Aea?aeaaiee oi?aa?neoao “Euea?anueea
iie?oaoi?ea” — ai?iaaaeaeaiiy a iaa/aeueiee i?ioean ia oaeoeueoao?
eiii’thoa?ieo oa ?ioi?iaoe?eieo oaoiieia?e; Oe?a?inueea aeaaeai?y
ae?oea?noaa — aeai?eoie o?eueo?aoe?? cia?aaeaiue, aeae?eaiiy eiioo??a oa
na?aaeiuei? e?i?? ?oeiienieo o?eoo?a.

Ai?iaaoe?y ?iaioe. Iniiai? iieiaeaiiy ? ?acoeueoaoe aeena?oaoe?eieo
aeine?aeaeaiue aeiiia?aeaeenue, iaaiai?thaaeenue ? io?eiaee noaaeaiiy ia
ui??/ieo iaoeiai-oaoi?/i?o eiioa?aioe?yo i?ioani?nueei-aeeeaaeaoeueeiai
neeaaeo Aea?aeaaiiai oi?aa?neoaoo “Euea?anueea iie?oaoi?ea”, a oaeiae ia
ianooiieo eiioa?aioe?yo: oeie?-nai?ia?? “?ania?aeeaeeaaiea ia?aaioee
eioi?iaoeee” (1985?.); Ananithci?e iaoeiai-oaoi?/i?e eiioa?aioe??
“Nia?aiaiiua i?iaeaiu yeaeo?iiaoaieee” (1989?.); 3-e Oe?a?inuee?e
eiioa?aioe?? c aaoiiaoe/iiai ea?oaaiiy “Aaoiiaoeea-96” (1996?.);
Oeie?-nai?ia?? “I?eeeaaei? i?iaeaie iaoaiaoeee oa ?ioi?iaoeee” (1996?.);
I?aeia?iaei?e eiioa?aioe?? “Ae?OEIOAOI” (1996?., 1998?.); I?aeia?iaei?e
iaoeiai-oaoi?/i?e eiioa?aioe?? “No/ani? i?iaeaie aaoiiaoeciaaii?
?ic?iaee ? ae?iaieoeoaa ?aae?iaeaeo?iiieo cania?a oa i?aeaioiaee
?iaeaia?ieo eaae??a” (1996?.); I?aeia?iaei?e eiioa?aioe?? “Parallel
Computing Technologies-97” (1997?.); I?aeia?iaei?e iaoeia?e eiioa?aioe??
“No/ani? i?iaeaie iaoai?ee ? iaoaiaoeee” (1998?.); Ia?o?e I?aeia?iaei?e
iaoeiai-oaoi?/i?e eiioa?aioe?? c i?ia?aioaaiiy OE?I?IA’98 (1998?.).

Ioae?eaoe??. Iniiaiee ci?no aeena?oaoe?eii? ?iaioe aeeeaaeaii a 23
ae?oeiaaieo i?aoeyo (a oiio /ene? 11 noaoae, c ieo 6 a ia??iaee/ieo
oaoiaeo aeaeaiiyo, aaoi?nueea na?aeioeoai).

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
/ioe?ueio ?icae?e?a, aeniiae?a, nieneo aeei?enoaieo e?oa?aoo?ieo
aeaea?ae ?c 149 iaeiaioaaiue ? aeiaeaoe?a. ?iaioa aeeeaaeaia ia 170
noi??ieao.

INIIAIEE CI?NO ?IAIOE

Anooi i?noeoue iaa?oiooaaiiy aeooaeueiino? ae??ooaaii? i?iaeaie.
Iaaaaeaii ia?ae?e caaea/, ae??oaiiy yeeo noa? iaiiaeeeaei aac cania?a
ia?aeaeueii? ia?iaee ? ianiaiai ia?aeae?cio. Iienothoueny ia?aaaae
canoinoaaiiy ia?aeaeueieo iaeii??aeieo no?oeoo? oa ?o oeie. Ee?oeii?
aaoiiaoe ioa?aeoa?eciaai? ye iaeii??aei? no?oeoo?e, ye? ia iathoue
cania?a eiiooaoe?? i?ae nai?ie aeaiaioaie, a eeoa iienothoueny i?aaeeaie
i?aenoaiiaee ?o noai?a. Oea aea? iiaeeea?noue nooo?ai ni?inoeoe ?
noaiaea?oecoaaoe i?eno?i? ia?aeaeueii? ia?iaee ?ioi?iaoe??.

Ia?oee ?icae?e i?enay/aii aiae?cia? aeine?aeaeaiue c ia?aeaeueii?
ia?iaee ?ioi?iaoe??. Cae?eniaii eeaneo?eaoe?th ?ia?o a iai?yieo
iaeii??aeieo ia/enethaaeueieo iiaeaeae. A ?acoeueoao? aiae?co
e?oa?aoo?ieo aeaea?ae aecia/aii i?noea iiaeae? ee?oeiieo aaoiiao?a
na?aae ?ioeo iaeii??aeieo ia/enethaaeueieo iiaeaeae. I?iaaaeaii
ii??aiyeueiee aiae?c a?aeiieo iiaeaeae ee?oeiieo aaoiiao?a c ??cieo
aaeocae ciaiue — o?ceee, iaoaiaoeee, a?ieia??. Aeae?eaii caaaeuei?
iniaeeaino? oeeo iiaeaeae oa ?ic?iaeaii eeaneo?eaoe?th oei?a iiaeaeae
ee?oeiieo aaoiiao?a. C?iaeaii aeniiaie, ui oai??y ia/eneaiue ia a?oiaiio
??ai? ia iaeii??aeieo no?oeoo?ao aac cania?a eiiooaoe?? i?ae aeaiaioaie
eeoa ii/eia? ?icaeaaoenue ? aeiaaa? eiiieaeniiai i?aeoiaeo.

Iiae?aia iiaeaeue ia/eneaiue ia iae?i??ai? noai?th? ?ioee i?aeo?ae
aei i?ia?aioaaiiy. Oae, a ?icae?e? aaiaeeoueny iiiyooy i?ia?aie, ui
neeaaea?oueny c ianooiieo /anoei:

Preacts — /anoeia, aea iienothoueny ?icaeooy ee?oeiiiai i?inoi?o ia
?aa?no?e oa a?aoiaioe a?eoiaoe/iiai ae?aco, yeee iaiao?aeii ia/eneeoe;

Inacts — /anoeia, a ye?e iaaeathoueny ii/aoeia? cia/aiiy aeayeei
iaeanoyi — a?aoiaioai;

Comacts — /anoeia, yea caaea? i?aaeea ia?aoai?aiiy aeaieo a eii??eao
?iai/iai i?inoi?o oa ?aa?no?ao;

Outacts — /anoeia, ui aeaco? eii?aeeiaoe iaeano? ?acoeueoaoo ia/eneaiue.

I?ioean ia/eneaiiy a?eoiaoe/iiai ae?aco cae?i/o?oueny oiae?, eiee
aeiaeia i?aaeei ia?aoai?aiiy aeaieo ia iiaea aooe aeeiiaii.

A ae?oaiio ?icae?e? caeeaaeaii oai?aoe/i? iniiae ee?oeiieo aaoiiao?a.
Iiaeaeue ia?aeaeueieo ia/eneaiue aac cania?a eiiooaoe?? i?ae aeaiaioaie
?icaeyiooi ia iniia? iiiyooy i?aenoaiiaie noai?a aeayei? aii?yaeeiaaii?
iiiaeeie. Aeey oi?iaeueiiai aecia/aiiy i?aaeea oa oiiae eiai
canoinoaaiiy aaaaeaii iiiyooy ee?oeiiiai oaaeiio. Ee?oeiiei oaaeiiii M
iaceaa?oueny ne?i/aiia i?aeiiiaeeia iiiaeeie Z2 aeaeyaeo:

M = (0,0), (i1,j1), …, (im,jm),

aea ik,jk Z. Oaaeii M(i,j), yeee ooai?th?oueny cnoaii oaaeiio M ia
aaeoi? (?,j), ?icaeyaea?oueny ye (i,j)-aa??aoe?y M(i,j) oaaeiio M:

M(i,j) = (i,j), (i1+i,j1+j), …, (im+i,jm+j).

Eiee aoaeaii aiai?eoe i?i canoiniai?noue i?aaeea, oi i?ae (i,j) aoaeaii
?icoi?oe eii?aeeiaoe oaaeiio ia aaoiiaoi?e ieiuei?. C iiiyooyi
canoiniaiino? i?aaeea iia’ycaia iiiyooy ?ici?oee oaaeiio M, aea eiaei?e
eiai eii??oe? a?aeiia?aea? iaeia cia/aiiy c aeayei? iiiaeeie noai?a Q:

lM=((0,0),q0), ((i1,j1),q1), …, ((im,jm),qm).

I?aaeeii ia?aoai?aiiy P ia iiiaeei? Z2Q iaceaa?oueny i?aenoaiiaea
ianooiiiai aeaeyaeo:

P: lM rM, (1)

yea aeaco?, ui iiiaeeia noai?a lM iaeiiiiiaioii cai?ith?oueny ia
iiiaeeio noai?a rM ia aeayeiio oaaeii? M.

Canoinoaaiiyi i?aaeea P (aai ia?aoai?aiiyi P) a eii??oe? (i,j) aoaeaii
aaaaeaoe eiai (i,j)-aa??aoe?th, yea iiaea aooe ae?aaeaia /a?ac
ia?aoai?aiiy aa??aoe?? oaaeiio ianooiiei /eiii:

P(i,j): lM(i,j) rM(i,j).
(2)

Aeey eiaeiiai i?aaeea (1) i?e?iaei?i /eiii aecia/a?oueny iaa?iaia aei
iueiai i?aaeei:

P-1: rM lM.

Aeey aa??aoe?? (2) oaeiae ?nio? iaa?iaia ia?aoai?aiiy:

P(i,j)-1: rM(i,j) lM(i,j).

A?aeiinii (i,j)-aa??aoe?e iia?aoe?y iaa?iaiiy caa??aa? «nai???aeio»
eiiooaoeai?noue, ine?eueee a?ae cai?ie i?noeyie i?aai? ? e?ai?
/anoeie i?aaeea iiiyooy (i,j)-aa??aoe?? ia caeaaeeoue:

(P(i,j))-1 = P-1(i,j).

sseui a aaoiiaoi?e ieiuei? iine?aeiaii aeeiio?oueny aeaa i?aaeea
P1(i1,j1) ? P2(i2,j2), oi ie aoaeaii iicia/aoe oeae oaeo ye
eiiiiceoe?th aa??aoe?e:

P3(i1,j1) = P1(i1,j1) * P2(i2,j2).

A?aeiia?aeii, P3(i1,j1) aoaeaii ?icaeyaeaoe ye aa??aoe?th i?aaeea P3,
yea ooai?eeiny a ?acoeueoao? eiiiiceoe??

P3 = P1 * P2(i2-i1, j2-j1),

ine?eueee eiiiiceoe?y aa??aoe?e i?aaee aea?aaeaioia aa??aoe?? ?o
eiiiiceoe??:

P(i,j) * R(i,j) = (P * R)(i,j).

Iaa?iaiiy eiiiiceoe?? aa??aoe?e a caaaeueiiio aeaeyae?:

(P(i,j)*R(k,n))-1 = R-1(k,n)*P-1(i,j).

I?aaeei R ae?acia a nenoai? P=P1, P2,…, Pn, yeui

(is,js)(R = Pk1(i1,j1)*Pk2(i2,j2)*…*Pkm(im,jm)),

aea PksP, s=1,…,m. Aeae? a ?icae?e? aeiaaaeaii oai?aio, yea
neeaaea?oueny c 12-oe oaa?aeaeaiue. Aiie ae?aaeathoue oiiae aeeiiaiiy
caeii?a anioe?aoeaiino? oa eiiooaoeaiino? i?e ??cieo aa??aioao
canoinoaaiiy i?aaee oa ?o aa??aoe?e.

Aano?aeoiei ee?oeiiei aaoiiaoii A ia ieiuei? Z2 iaceaa?oueny o??eea:

A = (S,Q,P),

aea S Z2 — ?iai/a iiea aaoiiaoo; Q — aeayea iiiaeeia noai?a, ye?
iiaeooue i?eeiaoe eii??ee ?iai/iai iiey S; P=P1, P2,…, Pn, — aeayea
iiiaeeia i?aaee ia?aoai?aiiy noai?a ?iai/iai iiey.

Iaeiicia/iee ee?oeiiee aaoiiao iiaeia ?icaeyaeaoe ye ooieoe?th:

A(P): QS QR, (3)

aea R S iaceaa?oueny iaeanoth ?acoeueoaoo ia/eneaiue.

Nenoaia i?aaee P=P1, P2, …, Pn aaoiiaoo A i?i?iaeueia ii e?eueeino?
i?aaee, yeui aeey aeia?eueiiai Pi P nenoaia PPi ?aae?co? ooieoe?th,
yea a?ae??ciy?oueny a?ae (3). Nenoaia P i?i?iaeueia ii e?eueeino? i?aaee
oiae? ? o?eueee oiae?, eiee aeiaeia i?aaeei Pi ia iiaeia ae?aceoe a
nenoai? PPi. Oaeei /eiii, a i?i?iaeuei?e ii e?eueeino? i?aaee nenoai?
iaia? «caeaeo» i?aaee.

Nenoaia i?aaee P i?i?iaeueia ii ia’?io i?aaee, yeui ia ?nio? oaeiai
i?aaeea Pj c oaaeiiii Mj, yeee no?iai aeeth/a?oueny a oaaeii Mi iaeiiai
c i?aaee Pi P, ? cai?ia Pi ia Pj a nenoai? P ia i?eaaaea aei ii?ooaiiy
ooieoe?? (3). Oeae aa??aio i?i?iaeueiino? aiai?eoue i?i oa, ui ia
iiaeia ciaioeoe oaaeii aeiaeiiai c i?aaee.

I?ae caaaeueiei iiiyooyi i?i?iaeueii? nenoaie i?aaee aoaea ?icoi?oenue
nenoaia, ui i?i?iaeueia ye ii e?eueeino?, oae ? ii ia’?io i?aaee
iaeii/anii.

Caaa?ooaaeuei?noue nenoaie i?aaee, ca cae/ae, icia/a?, ui ia ?nio?
iane?i/aiii? iine?aeiaiino? canoinoaaiue i?aaee, ye? iaeaaeaoue aeai?e
nenoai?.

O?ao?e ?icae?e i?enay/aii ieoaiiyi ?aae?caoe?? a?eoiaoe/ieo iia?aoe?e ia
ee?oeiieo aaoiiaoao. Iaa?oioiaaii ei?aeoi?noue a?eoiaoe/ieo oa eia?/ieo
iia?aoe?e. Ee?oeiiee aaoiiao A(P) ? ei?aeoiei, yeui a?i iaeiicia/iee oa
eiai nenoaia i?aaee aeey an?o iiaeeeaeo ii/aoeiaeo noai?a QS ?
caaa?ooaaeueiith.

sseui noai QR aeia?eueii? iaeano? R S a ee?oeiiiio i?inoi?? aaoiiaoa
?ioa?i?aooaaoe ye aeayea /enei, oi ei?aeoi? ee?oeii? aaoiiaoe iiaeia
aeei?enoiaoaaoe aeey a?eoiaoe/ieo ia/eneaiue. Aeiaaaeaii ianooii?
oai?aie i?i ei?aeoi?noue aaoiiao?a c nenoaiaie i?aaee aeey a?eoiaoe/ieo
ia/eneaiue a aea?eeia?e oa iaaaa?ia?i?e nenoaiao eiaeoaaiiy.

OAI?AIA 1. Aeey ia/eneaiiy a?eoiaoe/ieo ae?ac?a aeaeyaeo

f = (a1+a2+…+ak)*b /(2n-c)+d1+d2+…+dm

aneio?iiiee ee?oeiiee aaoiiao c nenoaiith i?aaee B1, B2, P0:

? ei?aeoiei ? i?i?iaeueiei aeey aeiaeaoi?o /enae a aea?eeia?e nenoai?
eiaeoaaiiy.

Cia/aiiy r, x, s i?ae ae?acaie i?aaee iaeaaeaoue ?aa?no?o, aeai? a yeiio
aeinooii? aeey eiaeii? eii??ee ?iai/iai i?inoi?o aaoiiaoa.
Cia/aiiyie xi=0,1 iicia/ai? a?oe /enae. *enei b=xkxk-1 …xm ?
aeiaeaoeiaee eiae xnxn-1…x0 /enea c caiineoueny a i?ii?aeie i?ae
neiaieaie r ? s a ?aa?no?.

C?iaeaii aeniiaie, ui aeey cae?eniaiiy iia?aoe?e iaae ae?enieie oa
eiiieaenieie /eneaie iaiao?aeii aeei?enoiaoaaoe iaaaa?ia?io nenoaio
eiaeoaaiiy c aaaith ?ic?yae?a: (-2)(i+j)/k. Aeey ae?enieo /enae k=1, a
aeey eiiieaenieo k=2. Ca oaeeo oiia ia? i?noea ianooiia oai?aia:

OAI?AIA 2. Aeey ia/eneaiiy a?eoiaoe/ieo ae?ac?a aeaeo

f = (a1 a2 … ak)*b /(-c) d1 d2 … dm

c ae?enieie /eneaie a iaaaa?ia?i?e nenoai? eiaeoaaiiy 1-ai ii?yaeeo,
aneio?iiiee ee?oeiiee aaoiiao c nenoaiith i?aaee B1, V1, V2 , P1 :

? noaiaie 0,1 ? ei?aeoiei ? i?i?iaeueiei.

A iaaaa?ia?i?e nenoai? 2-ai ii?yaeeo eiaeia eiiieaenia /enei iiaeia
i?aaenoaaeoe ye noio aaa ?ic?yae?a:

…, 4c, 4,-2c, -2, c, 1, -0.5c, -0.5, 0.25c, 0.25,… ,

aea n =wmetafile8? ????? ????????
?????????????yyy????.??????1?????? ??????? 
????&??yyyy?????Ayyy°yyy@????? ???&?
?MathType??0????u????????????-?????fH????Jy????u??
??????????-????Ry?????A????-??????E????X?&???X?&
???X?5 ???u?th??????Ia iniia? aaaaeaieo o oai?aiao i?aaee
?icaeyioo? i?eeeaaee ia?aoai?aiiy aea?eeiaiai eiaeo a iaaaa?ia?iee eiae
1-ai ii?yaeeo oa i?eeeaae iiaoaeiae aaaaoioa?iai? no?oeoo?e c ie?aieo
aeaioaei??ieo ee?oeiieo aaoiiao?a aeey ?aae?caoe?? iiiaeaiiy iao?eoeue.

A /aoaa?oiio ?icae?e? ocaaaeueiaii iiaeae? ee?oeiiiai aaoiiaoo. Cie?aia,
c?iaeaii ocaaaeueiaiiy iiaeae? ee?oeiieo aaoiiao?a, eiee eiaeia cia/aiiy
eii??ee yaey? niaith ae?enia /enei. I?e oeueiio aeiaeaoeiai aaaaeaii
i?aaeea R1-R3 ? aeiaaaeaii oai?aio.

OAI?AIA 3. Iine?aeiai?noue canoinoaaiue i?aaee B1,V1,V2, R1-R3:

aaaea A(P) o noai, a yeiio cia/aiiy an?o eii??ie, e??i ieaeiuei?
no??/ee, aei??aith? ioeaa?, a ieaeiy no??/ea i?noeoue eeoa neiaiee 0,1,
i?e oeueiio ?o iine?aeiai?noue ?ioa?i?aoo?oueny ye noia an?o /enae, ui
aoee caianai? a ee?oeiiee aaoiiao.

?icaeyaea?oueny ocaaaeueiaiiy iaaaa?ia?ii? iiaeae? ia aeiaaeie iayaiino?
aeaoaeo?a a ee?oeiiiio i?inoi?? aaoiiaoa. A iiaeaeue aeaoaeo?a aaaaeaii
iaai? iaiaaeaiiy. Ia aeiionea?oueny aeaio ae?aaiiaeueii-non?aei?o
aeaoaeo?a. Aaaaeaiiy aeiaeaoeiaiai i?aaeea aeicaieeei «no?eaaoe» /a?ac
aeaoaeoe.

I?iaiae?ciaaii aoaeoeai?noue ia/eneaiue. Anoaiiaeaii e?euee?noue e?ie?a
i?ioeano ia/eneaiue, yeui iaeeieoeyie caiiaiai? iaeano? aeaio oei?a, ui
iae/ano?oa aeei?enoiaothoueny.

Iienaii aaoiiaoeciaaio nenoaio aeey ?i?oaoe?eiiai iiaeaethaaiiy
ee?oeiieo aaoiiao?a. Iaaaaeaii no?oeoo?o nenoaie, neioaenen
oi?ioethaaiiy i?aaee oa aaaaeaiiy aeaieo, aeai?eoie ?iaioe iniiaieo
iiaeoe?a oa oi?iaeueio iiao aca?iiae?? c nenoaiith. I?eeeaaee ?iaioe
nenoaie i?i?ethno?iaaii a aeiaeaoeo 1. A aeiaeaoeo 2 iiaeaii aeoe
ai?iaaaeaeaiiy nenoaie.

INIIAI? ?ACOEUeOAOE OA AENIIAEE

A ?iaio? ?icaeiooi oai??th aneio?iiieo ee?oeiieo aaoiiao?a aeey
aeeiiaiiy a?eoiaoe/ieo ia/eneaiue c ae?enieie oa eiiieaenieie /eneaie ia
a?oiaiio ??ai?, ui aeaei iiaeeea?noue canoinoaaoe aneio?iiii-ia?aeaeuei?
aeai?eoie ia?iaee ?ioi?iaoe?? o eiie?aoieo ai?iaaaeaeaiiiyo. Iniiai?
?acoeueoaoe ?iaioe iieyaathoue o ianooiiiio.

1. Iaa?oioiaaii aeioe?euei?noue aeei?enoaiiy ee?oeiieo aaoiiao?a, oiaoi
i?eno?i?a c iaeii??aeiith a?o?oaeoo?ith, ye? i?aoeththoue ia iniia?
i?inoeo i?aaee i?aenoaiiaee ia noaiao nai?o aeaiaio?a aeey aeeiiaiiy
aneio?iiii-ia?aeaeueieo aeai?eoi?a ia?iaee ?ioi?iaoe??.

2. Cai?iiiiiaaii oi?aa?naeueio iiaeaeue ee?oeiiiai aaoiiaoa aeey ianiaeo
aneio?iiii-ia?aeaeueieo a?eoiaoe/ieo ia/eneaiue, ui aeaei iiaeeea?noue c
?aeeieo iiceoe?e i?aaenoaaeoe aneio?iiii-ia?aeaeuei? a?eoiaoe/i?
ia/eneaiiy ia ee?oeiieo aaoiiaoao iacaeaaeii a?ae nenoaie eiaeoaaiiy.

3. Ia iniia? aaaaeaii? iiaeae? ciaeaeaii oae? oi?aa?naeuei?
eiio?ao?aoe?? ?ici?uaiue ii/aoeiaeo aeaieo a ?iai/iio i?inoi?? aaoiiaoa,
c yeeo ?aae?caoe?y eiaeii? a?eoiaoe/ii? iia?aoe?? aeaiaeeoueny ye
/anoeiaee aeiaaeie, ui aeaei iiaeeea?noue aeei?enoiaoaaoe iaeio ? oo ae
nenoaio i?aaee aeey aeeiiaiiy ??cieo a?eoiaoeei — eia?/ieo iia?aoe?e.

4. A ?acoeueoao? ii??aiyiiy ??cieo nenoai eiaeoaaiiy ciaeaeaii
oi?aa?naeueio iaaaa?ia?io nenoaio i?aaenoaaeaiiy aeaieo (-2)n/r, yea
iaea?eueo i?aeoiaeeoue aeey a?eoiaoe/ieo ia/eneaiue ia ee?oeiieo
aaoiiaoao c ae?enieie oa eiiieaenieie /eneaie, aeicaiey? aaanoe i?aaeea
ee?oeiiiai aaoiiaoa, ye? ia caeaaeaoue i? a?ae ciaeo, i? a?ae
?ic?yaeiino? /enae, ui caa??aa? i?eioeeie iaeii??aeiino? ?
ia?iuoaaiino?. Oea aea? iiaeeea?noue i?i?i?coaaoe i?eno??e, a oaeiae
aanoe ia?aeaeuei? ia/eneaiiy c /eneaie aeia?eueii? aeiaaeeie, ia
ci?ithth/e aeai?eoi?a ia?iaee ? aeeiai?/ii ?iciiae?eyoe ?ano?ne
“ia?iaeyth/i? iai’yo?” i?ae ??cieie caaea/aie.

5. Aeiaaaeaii ei?aeoi?noue ciaeaeaieo nenoai i?aaee ee?oeiiiai aaoiiaoa
aeey a?eoiaoe/ieo ia/eneaiue c ae?enieie oa eiiieaenieie /eneaie, ui
i?aeoaa?aeeei a??i?noue a?iioace i?i iiaeeea?noue iia?oii — aneio?iiii?
ia?iaee ?ioi?iaoe?? a a?eoiaoe/ieo ia/eneaiiyo.

6. C?iaeaii ocaaaeueiaiiy iiaeae? ee?oeiiiai aaoiiaoa ia aeiaaeie
aeaoaeo?a a ?iai/iio iie? oa aeiaaeie eiioeioaeueieo noai?a eiaeii?
eii??ee, ui aea? iiaeeea?noue i?aeaeueoe iaae?ei?noue oaeeo i?eno?i?a, a
oaeiae i?aeaeueoe ?o nooi?iue ?ioaa?aoe??.

7. Noai?aii aaoiiaoeciaaio nenoaio aeey ?i?oaoe?eiiai iiaeaethaaiiy
i?ioean?a canoinoaaiiy i?aaee ee?oeiiiai aaoiiaoa, yea aeaea
iiaeeea?noue ia?aa??eoe aeanoeaino? nenoai i?aaee, a?aei?aoethaaoe
aeai?eoie aneio?iiii? ia?iaee ?ioi?iaoe?? a ?aieao cai?iiiiiaaii?
iiaeae?, ioe?ieoe aoaeoeai?noue ia/eneaiue ia ee?oeiieo aaoiiaoao, a
oaeiae noai?eoe aneio?iiii-ia?aeaeuei? aeai?eoie aeey ae??oaiiy ?ioeo
caaea/, ui aeaei iiaeeea?noue aeei?enoaoe ?? a eiie?aoieo
ai?iaaaeaeaiiyo.

Ioae?eaoe?? ca oaiith aeena?oaoe?eii? ?iaioe

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22. Oaa?e E.I., Ca?aeii Ae.Ae. Aeeaeiaiaay eioi?iaoeeiiiay nenoaia ia
aaca NI-4 aeey aiaeeca eciaiaiee a ninoaeenoie nenoaia /aeiaaea ia
iniiaaiee iaoiaenoieiae/aneiai enneaaeiaaiey // ?ania?aeeaeeaaiea
ia?aaioee eioi?iaoeee: oac. aeiee. e niiau. 5-e Ananithc.
oeieu-naieia?a.- Eueaia, 1985.- *.1.- N. 184-185.

23. *aaai A.E., Aeeue E.A., Eocueiye A.Ae., Ca?aeii Ae.Ae. Iauee
iiaeoiae e aiaeeco yeaeo?e/aneeo iaoei // Oacenu aeieeaaeia Ananithc.
iao/.-oaoi. eiio. “Nia?aiaiiua i?iaeaiu yeaeo?iiaoaieee”.- *.1.- Iineaa,
1989.- N. 121-122.

Iniaenoee aianie. Iieiaeaiiy, ye? neeaaeathoue nooue aeena?oaoe??, aoee
noi?ioeueiaai? ? ae??oai? aaoi?ii naiino?eii:

1. ?ic?iaea nenoaie i?aaee ooieoe?iioaaiiy ee?oeiiiai aaoiiaoa aeey
?aae?caoe?? a?eoiaoe/ieo iia?aoe?e c aeiaeaoi?ie /eneaie a aea?eeia?e
nenoai? eiaeoaaiiy [2,8,16,19].

2. ?ic?iaea nenoaie i?aaee ooieoe?iioaaiiy ee?oeiiiai aaoiiaoa aeey
?aae?caoe?? a?eoiaoe/ieo iia?aoe?e iaae ae?enieie /eneaie a iaaaa?ia?i?e
nenoai? eiaeoaaiiy ia?oiai ii?yaeeo [1,9].

3. ?ic?iaea nenoaie i?aaee ooieoe?iioaaiiy ee?oeiiiai aaoiiaoa aeey
?aae?caoe?? a?eoiaoe/ieo iia?aoe?e oa ae?ac?a iaae eiiieaenieie /eneaie
a iaaaa?ia?i?e nenoai? ae?oaiai ii?yaeeo [14].

4. ?ic?iaea nenoaie i?aaee ooieoe?iioaaiiy ee?oeiiiai aaoiiaoa aeey
ia/eneaiue iaae ae?enieie /eneaie i?e iayaiino? aeaoaeo?a ?iai/iai
i?inoi?o aaoiiaoa [5,13].

5. Aeiaaaeaiiy ei?aeoiino? aneio?iiieo ia/eneaiue ia ee?oeiieo aaoiiaoao
a aea?eeia?e oa iaaaa?ia?i?e nenoaiao eiaeoaaiiy [1,2].

6. Aeanoeaino? iia?aoe?e eiiiiceoe?? oa aa??aoe?? i?aaee ia?aoai?aiiy
noai?a aaoiiaoiiai i?inoi?o [6].

7. Ocaaaeueiaiiy iiaeae? ee?oeiiiai aaoiiaoa ia aeiaaeie ae?enieo
cia/aiue eii??ie [10,15].

8. ?ic?iaea i?eioeei?a ooieoe?iioaaiiy aaoiiaoeciaaii? nenoaie aeey
iiaeaethaaiiy aneio?iiieo aeai?eoi?a [3,4,7,21,22].

9. Ia?aa??ea aeai?eoi?a aneio?iiii? ia?iaee ?ioi?iaoe??
[11,12,18,20,23].

Ca?a?ii Ae.Ae. Ia?aeaeuei? a?eoiaoe/i? ia/eneaiiy ia ee?oeiieo
aaoiiaoao. ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.13.06 — Aaoiiaoeciaai? nenoaie oi?aae?iiy oa
i?ia?aneai? ?ioi?iaoe?ei? oaoiieia??. Aea?aeaaiee iaoeiai-aeine?aeiee
?inoeooo ?ioi?iaoe?eii? ?io?ano?oeoo?e, Euea?a, 1999.

Aeena?oaoe?y i?enay/aia ae??oaiith eiiieaeno i?iaeai, ye? iia’ycai? c
?aae?caoe??th a?eoiaoe/ieo ia/eneaiue ia ee?oeiieo aaoiiaoao.
I?iaiae?ciaaii aeine?aeaeaiiy c ia?aeaeueii? ia?iaee ?ioi?iaoe?? ?
aecia/aii i?noea ee?oeiieo aaoiiao?a na?aae an?o iiaeaeae ia?aeaeueii?
ia?iaee. ?ic?iaeaii oai?aoe/i? iniiae iiaeae?, ui aeine?aeaeoaaeany a
i???ioaoe?? ia a?eoiaoe/i? ia/eneaiiy. Aaaaeaii ? oi?iaeueii
iaa?oioiaaii nenoaie i?aaee ia?aoai?aiue aeey aeeiiaiiy a?eoiaoe/ieo oa
eia?/ieo iia?aoe?e, a oaeiae aeey ?aae?caoe?? neeaaeieo ae?ac?a oa
ianiaeo ia/eneaiue. Aeine?aeaeaii ?o ei?aeoi?noue ? i?i?iaeuei?noue.
Aaaaeaii ocaaaeueiaiiy ee?oeiieo aaoiiao?a. Iienaii nenoaio
iiaeaethaaiiy ee?oeiieo ia/eneaiue, ui ?aae?ciaaia aaoi?ii.

Eeth/ia? neiaa: ee?oeiiee aaoiiao, ia?aeaeueia ia?iaea, a?eoiaoe/i?
ia/eneaiiy, ?i?oaoe?eia iiaeaethaaiiy, aeai?eoi ia?aeaeueieo
i?aenoaiiaie.

Ca?aeii Ae.Ae. Ia?aeeaeueiua a?eoiaoe/aneea au/eneaiey ia eeaoi/iuo
aaoiiaoao. ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.13.06 — Aaoiiaoece?iaaiiua nenoaiu oi?aaeaiey e
i?ia?anneaiua eioi?iaoeeiiiua oaoiieiaee. Ainoaea?noaaiiue
iao/ii-enneaaeiaaoaeueneee einoeooo eioi?iaoeeiiiie eio?ano?oeoo?u,
Eueaia, 1999.

Aeenna?oaoeey iinayuaia ?aoaieth eiiieaena i?iaeai, naycaiiuo n
?aaeecaoeeae a?eoiaoe/aneeo au/eneaiee ia eeaoi/iuo aaoiiaoao. Auiieiai
aiaeec enneaaeiaaiee ii ia?aeeaeueiie ia?aaioea eioi?iaoeee e
ii?aaeaeaii ianoi eeaoi/iuo aaoiiaoia n?aaee anao iiaeaeae ia?aeeaeueiie
ia?aaioee. ?ac?aaioaiu oai?aoe/aneea iniiau enneaaeoaiie iiaeaee a
i?eaioaoeee ia a?eoiaoe/aneea au/eneaiey. Aaaaeaii e oi?iaeueii
iainiiaaii ianeieueei nenoai i?aaee i?aia?aciaaiee aeey auiieiaiey
a?eoiaoe/aneeo e eiae/aneeo iia?aoeee, a oaeaea aeey ?aaeecaoeee
neiaeiuo au?aaeaiee e ianniauo au/eneaiee. Enneaaeiaaia eo ei??aeoiinoue
e ieieiaeueiinoue. Aaaaeai e eco/ai ?yae iaiauaiee eeaoi/iuo aaoiiaoia.
Iienaia ?aaeeciaaiiay aaoi?ii nenoaia iiaeaee?iaaiey eeaoi/iuo
au/eneaiee.

A ia?aii ?acaeaea i?iaaaeai aiaeec ?aaio ii ia?aeeaeueiie ia?aaioea
eioi?iaoeee. I?aaeeiaeaia eeanneoeeaoeey ?aaio a iaeanoe iaeii?iaeiuo
au/eneeoaeueiuo iiaeaeae. Ia iniiaa aiaeeca enoi/ieeia eeoa?aoo?u
ii?aaeaeaii ianoi iiaeaee eeaoi/iuo aaoiiaoia n?aaee ae?oaeo
iaeii?iaeiuo au/eneeoaeueiuo iiaeaeae. Inouanoaeai n?aaieoaeueiue aiaeec
ecaanoiuo iiaeaeae eeaoi/iuo aaoiiaoia a ?acee/iuo iaeanoyo ciaiee —
oeceea, iaoaiaoeea, aeieiaee. Auaeaeaiu iauea iniaaiiinoe yoeo iiaeaeae
e ?ac?aaioaia eeanneoeeaoeey oeiia eeaoi/iuo aaoiiaoia.

Ai aoi?ii ?acaeaea aeaiu oai?aoe/aneea iniiau au/eneaiee ia eeaoi/iuo
aaoiiaoao. Aeey oi?iaeueiiai ii?aaeaeaiey iiiyoey aaoiiaoiiai i?aaeea e
oneiaee aai i?eiaiaiey aaaaeaii iiiyoea eeaoi/iiai oaaeiia. I?aaeeii
i?aia?aciaaiey P ia iiiaeanoaa Z2Q, aaea Q — iiiaeanoai ninoiyiee y/aae,
iacuaaaony iiaenoaiiaea neaaeothuaai aeaea:

P: lM rM,

eioi?ay oeacuaaao, /oi iiiaeanoai ninoiyiee lM iaeiiiiiaioii caiaiyaony
ia iiiaeanoai ninoiyiee rM ia iaeioi?ii oaaeiia M. Aeaeaa a ?acaeaea
aeieacaia oai?aia, ninoiyuay ec 12-oe /anoiuo ooaa?aeaeaiee. Iie
au?aaeatho oneiaey auiieieiinoe caeiiia annioeeaoeaiinoe e
eiiiooaoeaiinoe i?e ?acee/iuo aa?eaioao i?eiaiaiey i?aaee. A ?acaeaea
aaaaeaiu oaeea iniiaiiieaaathuea iiiyoey, eae aano?aeoiue eeaoi/iue
aaoiiao, iaeiicia/iue eeaoi/iue aaoiiao, ieieiaeueiua ii /eneo
iiaenoaiiaie e ii iauaio nenoaiu i?aaee, caaa?oathuayny nenoaia i?aaee.

O?aoee ?acaeae naycai n ?aaeecaoeeae a?eoiaoe/aneeo e eiae/aneeo
iia?aoeee e n iainiiaaieai eo ei??aeoiinoe. Eeaoi/iue aaoiiao yaeyaony
ei??aeoiui, anee ii iaeiicia/iue, e aai nenoaia i?aaee aeey anao
aiciiaeiuo ia/aeueiuo ninoiyiee caaa?oathuayny. Aeieacaiu oai?aiu i
ei??aeoiinoe nenoai i?aaee aeey a?eoiaoe/aneeo au/eneaiee a aeaie/iie e
iaaaaeia?iie nenoaiao eiaee?iaaiey. Naeaeai auaiae i oii, /oi aeey
auiieiaiey iia?aoeee iaae aeaenoaeoaeueiuie e eiiieaeniuie /eneaie
iaiaoiaeeii eniieueciaaoue iaaaaeia?ioth nenoaio eiaee?iaaiey n aanaie
?ac?yaeia: (-2)(x+y)/k. Aeey aeaenoaeoaeueiuo /enae k=1, a aeey
eiiieaeniuo k=2. A iaaaaeia?iie nenoaia 2-ai ii?yaeea eaaeaeia
eiiieaeniia /enei iiaeii i?aaenoaaeoue eae noiio aania ?ac?yaeia: …,
4c, 4,-2c, -2, c, 1, -0.5c, -0.5, 0.25c, 0.25,… , aaea n =wmetafile8?
????? ???????? ?????????????yyy????.??????1??????
???????  ????&??yyyy?????Ayyy°yyy@????? ???&?
?MathType??0????u????????????-?????fH????Jy????u??
??????????-????Ry?????A????-??????E????X?&???X?&
???X?5 ???u?th??????A /aoaa?oii ?acaeaea naeaeaii iaiauaiea
iiaeaee eeaoi/iiai aaoiiaoa ia neo/ae, eiaaea eaaeaeia cia/aiea y/aeee
i?aaenoaaeyao niaie aeaenoaeoaeueiia /enei. A /anoiinoe, aeieacaia
oai?aia ioiineoaeueii ei??aeoiinoe e iaeiicia/iinoe aaaaeaiie nenoaiu
i?aaee. ?anniio?aii iaiauaiea iaaaaeia?iie iiaeaee ia neo/ae iiyaeaiey
aeaoaeoia a ?aai/ai i?ino?ainoaa eeaoi/iiai aaoiiaoa. Ia iiaeaeue
aeaoaeoia iaeiaeaiu iaeioi?ua ia?aie/aiey. A /anoiinoe, ia aeiioneaaony
iiyaeaiea aeaoo aeeaaiiaeueii-ninaaeieo aeaoaeoia. A ?acaeaea
i?iaiaeece?iaaia yooaeoeaiinoue au/eneaiee ia eeaoi/iuo aaoiiaoao,
onoaiiaeaia caaeneiinoue eiee/anoaa oaaia au/eneaiee io ?acia?a ?aai/ae
iaeanoe, caiieiaiiie aaeeieoeaie. A ?acaeaea oaeaea iienuaaaony
aaoiiaoece?iaaiiay nenoaia aeey eieoaoeeiiiiai iiaeaee?iaaiey eeaoi/iuo
aaoiiaoia. I?eaiaeeony no?oeoo?a nenoaiu, neioaenen ycuea iienaiey
i?aaee e enoiaeiuo aeaiiuo, aeai?eoiu ?aaiou iniiaiuo iiaeoeae e aeeaeia
n iieueciaaoaeai. I?eia?u ?aaiou nenoaiu i?ieeethno?e?iaaiu a
i?eeiaeaiee.

Eeth/aaua neiaa: eeaoi/iue aaoiiao, ia?aeeaeueiay ia?aaioea,
a?eoiaoe/aneea au/eneaiey, eieoaoeeiiiia iiaeaee?iaaiea, aeai?eoi
ia?aeeaeueiuo iiaenoaiiaie.

Zerbino D.D. Parallel Arithmetic Computations on Cellular Automata.
Manuscript.

Thesis for Degree of Candidate of Technical Sciences in speciality
05.13.06 — Automatic Control Systems and Progressive Information
Technologies. State Scientific Institute of Information Infrastructure,
Lviv, 1999.

The dissertation is devoted to the solution of the complex problems
connected with realization of arithmetic computations on cellular
automata. The analysis of achievements in parallel information
processing is fulfilled and the place of cellular automata between all
parallel processing models is determined. Theoretical base of
investigated model oriented on arithmetical computations is developed.
Systems of replacement rules for realizing logical and arithmetical
operations as well as for evaluating the complex expressions and massive
computations are introduced and formally grounded. Their correctness and
minimality are investigated. A number of generalizations of cellular
automata is introduced and studied. Realized by the author system for
simulation of cellular computations is described and realized.

Keywords: cellular automata, parallel processing, arithmetical
computations, simulations, parallel substitutions algorithm.

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