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accece ycoe peec ep oca aae XX ea .. ao, cpay e ycope x pocey opy oyeu, aoap oopo accopyc a co. p acceco ycoo peece cxoo ee papae, aae yco, oopo coeaec c cooe papaee, aae eyco. Baae yco papae ae ca oe ooe aoo; eyco papae poopye ypy pea e aoo o o peapeoo oye. B peyae pao ycooo peeca yco papae popeae cocooc a o c, o o oe. oo, o opaoaac ycoa c, o ec pooo oyee, yco papae oe oppepoa c eyco, peecy ey a eoop pec poeyo pee.

o aaa eyeo coe oco epoooo epo, o appy peeca poeae epe cyeceo epepe epo a. oe caca, e ey epoa, ocpeco oopo o o aoecoa, ec cpaeo o.

cceoa, ycaaae ae caca eo po epo aoc, oe a pyee eo ac ooo cpo apo eppoo (18571952). Paoa eppoa apaaa oeeec ypoe, a e epoooec. Te e eee, aaa peeopx ec coa, oe oe o cye paaa ocoe p pao caca.

ep oa pacp cepe aaoeco opaa oa oo oec cceoa Cao Pao--axa (1911). pe eo opac epoo co cepepa, papaoa paee ao o (cepepo paeo poae epo, o e poae pye e oa), axa ye, o o ee eoy apxeypy. poe epoo coca oa xo paoopae ae e, oe oope y yacye peapaox poeccax. axa oca epo a opoae e, oope oya ca co paee opoca, oy aae epo, a oca opa epaee opoca, aa acoa (c. pc. 7).

Pc. 7. Aca epx eo oooo oa eoea Opaae o o ooo opooe paoopae epoo o ope ea, paeeoc epo ac e acoa. axa pa ey ea c opo acoa, aoecy c coce epoa, ea c acoa, poepyc pye yac oa.

Hecop a pa cpoe, ce epo poo opa oaoo. opa epeaec o acoa e opox epecx yco, a aaex oeao ec, aya oopx cocae ooo 100 B, a eoc 1 c. Booee yco ca c ee ooeo apex oo ap epe oepxocy eoy epay eeoo oc yp e, ee oay.

oepa ap eeoo pocpace pepo 10 pa oe eo ypeoo oepa. B coco oo oepaec pacepaa paoc oeao ooo 70 B. p o o ap poa ey eeo, a a ocy ya x opae coca epa. eca xeca cy, eopya epay, yeae ee poaeoc oo ap. oo ap yp e ee cee eopye epay, ea ee ce oee poaeo.

oa ocaec eoopoe pecoe aee oeaa, aaeoe opoo, ooea opaa c po peeepa ca, peyae oopx a paoc oeao eec a poooo, o ec ypeee coepoe e caoc ape ooeo o ooe ee cpee. peo epe 1 c poaeoc epa ap aae pacepa oea opaaec coey ae coco oo 70 B. oce aoo aoo pa epo ocaec a ecoo cey pepa, o ec apea poaeoc epa o epo e oe ec. o ae pee acoe eepa yco e oee 200 pa ceyy.

Xo aco oxo a pooa, yc o poo ae. x aee xapaepc eae: copoee o oc co eo, a epaoe copoee co ao. ooe ap pacceaec ye epe 12 . o peooea pacco, cocae oa ecoo caepo, yc o peeeppoac. Heoxooc oopo yca o opaae acay copoc pacpocpae epoo yca o acoy o /c.

C ey epoa oocpeyc xec epeaa epoeaopa ec ooa opoco epoo cacax. oa oea ec ocae ooa acoa, oey eaopa xo ypeox aex ypo, e o xpac, caecy e pocpaco po 20 ey epaa pecaeco occaeco eo. oa oyee ocae a, aaec ooppoaoe eee oey epoeaopa.

Bcooec oey epoeaopa cac c peeopa occaeco epae, o ee ee poaeoc. e ye oya, ec eee apa pae epa oea opoy eeppoa yca. Ec e epaa capyec a ypoe oeaa oo, e ye opo.

a cac ae eae e a aoc acoa epoa. o ycaoac ecoc xoa, a epo oe epepo eppoa o 1000 caecx xoo.

Ee aae ea epoooa caa ca ceo aa po caco oye. Ca oa, poxo epe x, oy pao cee ycac ocac. Opaae a ce ae ao a. Mo oopoeoo o pocoo eoea coepa pepo oaooe oeco epoo. Ho oo o pocoo eoea oaec yopoeoc eepox caecx ce. o-oy, oyee oa ec poecc ee apxeyp epoo ce, copooae acpoo caco.

2.2. Caoee pae HC Haoee e pecaec ceyee opeeee HC a aao a, aoe [6]:

cyccmea epoa cem mo cyecmeo napaeo pacnpeee npoeccop, omop oaaem cnocoocm coxpaeu u penpeemauu onmoo au. Oa cxoa c oo yx acnemax:

1. aue npuopemaemc cem npoecce oyeu;

2. coxpaeu au ucnoymc cu eepox coeueu, aaee mae cuanmuecuu ecau.

cop HC aaec 1943, oa Maao c peo oe opoooo oecoo epoa oaa, o a y, oopa oe cea a epoo-ceo ae, oe ae cea ce epoo [7]. Ca xi, ocyae a xo epoa, yoac a ecoe oe wi (caece eca). aee o cypyc, peypy ca, cy a ey cee wn S = xi + w0, (2) w i i=oaec a xo oa, peayeo aaoy y epoa.

Pc. 8. Moe epoa Tpaoo aaoa y ee cyea , o ec ca a xoe epoa y oec oa, oa cyapoe xooe oece peae eoopoe pecoe aee.

Pc. 9. T aaox y epoo Xe [8], ya eoe exa eeoc oa, copypoa pao oye, oopoe yeae cy c ey pe- occaec epoa, ec aoc oox coaae o pee.

pya oe oye paax oee pao apxeyp ce, aao epepoo, a peoea yceo peea oepoa pao peoo paa Poeao [9].

B coe cao poco epc ooco epepo (c. pc. 10) pecae coo ce c o xo, o xo o oee ype , a oop, cp co epoo. Oe epo cex oocox epepoo ec poapaeoc ce, xapaepyac epeae opa o xooo co epe K cpx coe xooy co. B caapo ooo, ye ( i coe k, (k=1,...,K+1) coeec ocpeco eco wijk ) co ce j ya peyeo co k1. ec k=0 k=K+1 ooaa, cooeceo, xoo xoo co.

Pc. 10. Cxea poapaeo coo HC Mopoae epc oy e pe c ey ece co, c peeax ooo co, xaoe c ey co eco peypx.

Bxoo co epepoa cy pea pepac xox cao a epo cpoo co. B cpx cox pocxo ocooe eeoe peopaoae opa, a xoo co ocyece cyepo eex cao oceeo cpx coe. B aece eeoc y cpoo co coy epepyee coae y f (S)= (3) 1+ e-S o oyee epepoa oa eeapae poecc ee ae eco ecox caecx ce, epao oope o ex op, oa ce e popee eoxoe coca.

B ocoe oye e cooae pepoox ax, oeex ao (c. pc. 11).

Pc. 11. opopyeoe oyee HC a ao X,D ae ce eop ecx xox cao ce X = (X1, X2,, XV ) cooecy ey eop eaex xox cao D=(D1,D2,,DZ). B poecce oye a xo HC oceoaeo oac ae pepoooo aopa aoo ={X,D,q = 1,Q}, oce eo cec oa ey aeq c Y = (Y1,Y2,...,YZ ) eae xoa ce e = Yq - Dq. (4) ec o opo oo oa eoo paccoe ey eopa Y D.

aee, c oo opeeeoo paa aopa pocxo aa oa acpoex apaepo ce, o a oa yeaac. poecc oopec o oce ce cocooc o eae peopaoa xo-xo, aaoo eo e pepoo aopo aoo.

aoap oye ce popeae cocooc pao peapoa e oo a ao, peee poecce pepo, o ae xopoo cpac c py aopa ax oycoo pocpaca xoo, oope oa oa e ea paee. B o cce oop, o HC oaae coco ooe (generalization).

Oa ooe, cea ea eco a xoe ce, ee e cocae. epa x oycoea eocao aeco apoca, oeo ce oex paepo. Bopa aa eooo opa, peeo ce poecce oye, -a opaeoo oea oyae op.

Poeaa ca ecox caecx ce eac acoc o oo, acoo oo xo epepoa coaa c xo aoo, cooec co cey pao oye. Beca ce yeuuamc, ecu xoo cua, copupoa npuuau epoo, cuo ca, u yeamc, ecu o cuo cou. Oao, o pocoe pao a o peo oo poapae ce e cpx coe.

Hecoo oe Mc eep o yo aa ceo ooc oocooo epepoa.

e x coeco epcepo [10], peaaeo ec ocpy a eop epox cee, ox oecypaa pe ypae epeca epo ce. aaoc, o ec ce e oy peaoa ae XOR-y (oeca y caee Ȼ, oya c eo py aopo [10] cayc eca p cceoa cpaeo eoc pepooAop opaoo pacpocpae o a 1. aa eco cee.

( k Beca wijk ) cee wi(0 ) o cex cox aac cya opao a aee e, apep, epae o 1 o +1.

a 2. pecaee ooo xooo eopa X cooecyeo eaeoo xooo eopa D.

a 3. po poxo: pace aecoo xoa.

Bcee xoa Yi(k ) i-o ya k- cpo coe, k=1,...,K, Yi xoo coe:

Hk- k ( Yi(k ) = f wi(0 ) + wijk )Yj(k -1)(k = 1,..., K), e Yj(0) = X, j j= H K K +1) Yi = f wi0 + w( Yj(K ).

ij j= ec Hk oeco yo k- cpo coe.

a 4. Opa poxo: aaa eco opoo.

cooae peypcoo aopa, aaeoc a xox yax opaaeoc epoy cpoy co:

( ( ( wijk )(t +1)= wijk )(t)+ ik )Yj(k -1)(k = 1,..., K +1) ( k=K+1 e ik ), oca oy, ece:

(K i +1) = (Di -Yi )Yi(1-Yi ) eo oo peypco oca cex pyx cyae:

( k ik ) = Yi(k )(1-Yi(k ))(jk +1)w(ji +1)(k = 1,..., K).

j Oe, o e Yi(k )(1-Yi(k )) ec pooo coao y ooceo ee apyea. Ec coyec pya opooa y, o e eoxoo e. Oya apaep oo paec epae o 0 o +1.

a 5. oopee o aa 2.

x poeyp), x cee cocooc co opae.

Bxo oo ooe oaee cpx coe c ee epoa ece oa, oao e o coc, a acpo eca y ao ce.

Haco popecc ocy oce oo, a Pyexap, Xo Bc 1986 oceoaeo epeop Aop Opaoo Pacpocpae o (AOP) [11, 12], epe oca Bepoco 1974 oy [13].

eco ae co pao oocpcx yex [14,15], eaco oopeeo c Pyexapo peox oe AOP Aop oceoo yopoa oye epoo ce.Xo AOP pacce ecc o oooc oye oocox cee, o, e e eee, e ca cpyeo, oop oo pe opeo opoc cea epox cee oay oa cpyyp apaepo ce. aa aax apaepo ce ocyecec ec cya opao, a ca AOP, ec cace a eo coxaceco apoca, ec o coe cy e oee e oa eoo cy oo e apapye ooa poecca oye oe oaoo cpeya. Bece c e, e ae coe, o oa (4), coyea oe aeca HC, ec oocpeao ye apaepo ce, ooy oca ee ya peyec, cooeceo, oa eo.

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