AJITEBPA H JIOTHKA CeuHHap TOM HI BunycKH 5-6 PyKOBOflHTent A.H.MajcbiieB 1964 r. OACC CBEJEHMfl V 3"V B.Q.KOCTHpKO I. IOKTOP j.s.denton*) B nhcbme asiopy (uaft 1964 r.)f coaepaaods op HOBHX pesyjibtaiob no CBefleHmo npodjiemu pa3pemn«octii(takae 0 HeonyOraiKOBaHHux, CM. B [2] ), ykasusajt, qio He pemena aaaaia 0 paspeiflhmocth (OTHOCHT6JIBHO BUHOJIHilMOCTH H BUnOJIHHMOCTE B KOH61 - HEX MoaeJiJDc) Knacca saukhyticc $opwyji yakoro acihcjieahh Huenomx B npeabapehhoh $opue cjiesyioinha BUB:,yi,...yn,z)f (I) napo A/ coaepaht e^hhctbehhaa fflbyxuecrahb npeahkai :F. 3aeci> (Syaei aokasaaa TEOPEMA I. Knacc fopwyn y0ii BH^a ( I) H B J I H 6 T C H K JI a C C 0 M C B e f l C H H H 3JIH B M - H O J I H H M O C T H H 7(J I H K O H e ^ H O f l B U II 0 JI H H- M 0 C T H. Ilpw STOM KJiacc $op«yji K yffll aaaubaeich KJiaccou cseaehhh fljih BMnOJIHHUOCTH (^ItH KOHe^HOH BHIIOJIHHMOCTH), 6CJQI MOXHO yk83at nosbojiflioipa BJIH JiB<3ofi $ophyjoi yidn <^ HaBiH B /T pas- (KoaeiHO pabh03ha?hy») $opuyjiy &. $opuyjiu xe 6C H HaSHBaBTCH pabhoshaqhumh (KOHeUHO pabhoshaihmih ), 6CJIH OL (BunoJiHraia B KOHCTOOB uoaejoi) Toraa H TOJIBKO loraa, Kor- BunojiHHwa (BbmojiHHua B KOHeiHoM Moaena). #JIH x) MaTeuaTHiecKHH $akyfliiet yhhsepchteia MaK-PHJOia, Kanaja.
B.O.KOCTHPKO aiofi TeopeuH HcnojiBayeii cjieaybny» TEOPEMy 2. K n a c c $ o p i i y a y H ft Vz M(?fr,.,-%; x.,1), (n) coaepxaihx I I O U H M O oahowecthbix n p e - a H K a T 0 B eahhctb-ehhhtt a B y X M C C T H H f i n p e a H K B T, H E J I H C T C H KJiaccou c B e a e - H U H a * H B U n O J I H H M O C T HCA.S.Eahr^OKTOpCKafl flhccep- TOUHH, MaccaiyceTCKHg TexHOxorH^ecKHi} HHCTHTYT, Iy62) H a a H KOHe^HOa BHnoJIHHMOCTH (A.S.Kahr,Hao Wang,C006 - BieHO asiopy J.S.Denton'OM). B CHxy Teopeim 2 AJIH AOKaaaTeJiBCTBa xeopeuu I aoctaioqho yna- 38TB ajirophtm, nosbojihbmhm ajifl a»(5o0 $opuyjra 6^- BHA& (n) HaflTH HeKOTOpyn pabhoshaihyc eft gopuyoy &i_ H nekotopyn KoneiHO pabho- (I). Ilycii $opuyjia (II) BunonHHaa B HeKOiopoB pacciiotpmi KJiacc $opnyji 2. (CM. [ij, ctp. 105 H ^To(5u noctpohtb fopwyny BHaa (ID), pabhosaaihyb $opuyae (0) (cha^ajia c npeahkaiom pasehctsa), nociynmn cjieay»mhm ofipasom., a auehho: conociabhu oahosnaqhiai ocipasom Kaxaua npeaa- K8T Vi C H6KOTOPHM 3JieMeHTOM (JJ\ SjieMeHTH ^,...^e HO - napho paajihihu n He nphhaanemai 7. Ha 7 '- ^c* ( i/4-r, <^e } on - a npeahkai 0', ncuioxhb aan nndux ", ecjm x=yy^_, 0 - B ocranbhhx <ie pea /\/(Jr')Viy..iv^locfuli') pesyjibiai samehu B $opmyne A/f^%,-, 3&; ^#.z,) BHpaxeHna 5^x, ^.^, ^A^ cooibei- CTB6HHO na 7VAX; ^1^; ^x2 Toraa, oqebhaho,horahho yssepxaehae: Heipyano BOHHTB, ^TO $opmyna (n) pabhosha^ha cueaynmea $op-
KJiacc CBefleHMH V3 V uyjte: A H ) A (A x~v- AZ~ 3v0... TSK «e npocio HOCTPOHTB fopuyay BH^a (ffi) Sea npeamcata paseh-, pabh03haihyi) (H KOHeiHO pabhosha^ayn) $opmyjie (II): Ilpn noctpoehhh ie $opuyjm BE^a (I), pabhoshaihoft $opuyjie (2)^ BOB - HMKaeT TpyanocTB, CBHsaHHafl c Teu, ^TO B (I) Jiesee KBaHTOpos cyme- CTBOB3HHH ctoht IXx, a nail Haflo Bupa3BT $opwyjiofi BHga (I) cy - ajieuehtob y-i,-.-,^ (a Teu cauhm H npeamcatob )» OBHHX H Tex ae «JIH scex ^c. 3. nocienehho CTPOHTB $opwyjiy suna (I), pashobha^hyd $opuyne (n), H ee Moaem, 5- <y'j(p'>>y/^^{^,. OCosHaqHM qepea 3r:oci^z $opuyjiy ccy~ BxeiieHTH Q-,&eJ' Hasoseu HepasJiHMHMHMH aneueh TOII ce7' B MoaejiH S'=<y'J0'>, ecjw 0aa -tp'66, H 0-CO,^, I p a S H H ^ H U H 3JieueHTOMC-B npothbhom CJiywae. 3neueHtu oi^e jhasoseu B e p a a ^ H q u u i i u H B uoaejm 5', ecna OHH He pasjinihuu HH OJHHM ee aneueatou, n p a 3 n H- q H u u - B npothbhom cjijmae. MoaeJiL nasubaetch nphseseh- H o a, ecjm jno(3ue asa pasjuwhux ee ajiemema pasjmqhiiu B neit. BH2HO, ecjui $opuyjia Buna (I) aueex uosejn>, TO OHa Hueei a rje 7^ ecu. $opwyjia ). (1) B jnodofl nprneaehhofi uoaejiii < J;6> $opuynh (iy) TaKOtt, qto Q 1^11/1=1., eflhhctbehhhft. JeMCTBHieJIBHO, B03BM6M jindoe on & 7 H TaKoe />e p',?to flflfl joodoro z e ^ ei MOCTO T^(&,ocfpi E). Ms (1) BHflHO, 1TO ^/Op - ^ H 1TO fljih JIB(5oro Z Koro, 1*0 &zz = i, aaewehth /? H z He pasjuramuh TOM x. Ho 3TO oshaqaei, ITO 01 n d H e ajreuehtbi a, 6e$ *
He pasjraqjimh sjieuehtom x~. TEK KSK x. - npohsbojibhhft sneueht, TO B uoseira </;6>> jrofiae ane - M6HTH Q.,^, TaKHe, 1TO OCLCL** 9 & B = i, H'epa3HH«IHHH. TaKmi odpasou, Han y^ajiocb BHpaaHTB ^opuyjioa BHfla (I) cymectbobahhe ne- KOTopro ajiemehia, eahhctbenhoro B jrodoft nphsesehhofl uozew aiofi $opmymi. UosTOMy onpeaeahu: ' Bcex 3C ^ ^ (1 ),...,t/^tj, B cany (1 ), otjinqaiotch OT ^. ITO- OHH OTJiMiaJtHC!) a. OT <//2^..., ^, nojiaraeu: Bcex jc.+^i),-,...f HeipyaHO sawemtb, ^TO B jnodoa nphbeaehhom MOflerai i/,,...,^zx (O - KOHtiOHKiaiH $opmyjm (1 ) H cjiesyromea K: i//^, TaKHe, ^TO JJIH nekoioporo ^c, H JJIH JOBdoro z HMeei MecTo Tz (0 ; x-,yi,.--, vt, z) - OSHM M ie ace SJIH seer x, IITO Han KSK pas H TpedyeTca. onpesenehae MOSCJIH -5' Tan, qiocu B ne8 fiima Qpi+iti-*, i=l,.~,t-i, (3 ) BO Bcex cyqahx, Kpoue(1 ) H (3 ) i^i,...^. (4 ) TaK KBKflHaroHaJiBHue SHaqeHHH npeflhkaia 0 yae onpeseaenh Hesa- BHCHMO OT 0, TO aharohajibhhe SHa^eHHH npeflhkaia f> B uoaejih 5 ' cjieflyknqjm odpaaou: (5 ) H3BOJIBHHUH. as npeshkaia </ % i=-t,2,... ; 6 j ociajibhhe (6 ) <3&' aa Ju^i^..^} BOSBUBM npo- 3 (?} \/i>...,v^z> oc, yt z)
Ejiacc cseaehhh V3"'V.. (1*) a lepes M± = M^( ', vz)... } v^2,<x-,y) ( cootbeictbehho, A^*A^^/...^Ar/^)$op«yay i noaynemiyi) us /V^ %,..._, ^ ; a:, ^ 2; cnaiajia aameaob. 2 na ^c (cooroetctbehho, z Ha y ), a aaveu sanehofi (1M). MOSHO (5uJio (3u nonasatb, ^TO $opuyjia 1/x Ji/i... i/t u l/z r,^; a:, t/i,..,kt,ky,z), (H) 7"3 - KOHHOHKEIHH $opwyji ( 1 ), (2) (t = ^2) H cjieay»-, B onpeflejiehhoft BBirae Moaemi 5 '= < J1; <P > } y/4,-,vt+2}. ecjih (n) BanojiHHua B Moaejra S (2) * (3 *), H fio- Jiee Toro, MTO ona pabhosha^na n KOHCIHO pabhosha^na $opuyjie (H). IIoflBJieHHe B (3*) BupaateHiia Mi, Mz, M3 BHSBano cae-. <Iopuyjia (n), Vz [M*A MZA (Z^OCA z~y M3 J, (4*) TaK KaK sxossehhh ^ococ., tyy, ^z z B pasjunihbie M3 Bupaate- (4*), B0o<5me robopn, He cobna^ant, TO STH BHpameHHH aamiajiu - pasjiwihue ycjiobhh HaflHaroaajiBHHe SHaweHHH npeankaia 0 uo- * 3', &>. B $opuyjie se (H) jharohtutthhe BHaqemiH npeaakaia ^ oimciiba»tch HeaMaroHanBHHMH shaqehhhmh npeanicata 0' ee $'>;Hau «e aaao BupasMiB $opuyaioh (JHE) see ycnoshh, $opuyaofl (n) Ha awarohajibhhe SHa^emin opeahkata 0. OciaeiCH ycipahhib npe^hkai pasenctba. IlyciB a): $opiiyxa (II) Bunoniania B KOHeiHoK (3): gopiiyxa (n) B0o(5me BunojiHHMa, HO He Bunoxmiua HH B oanofi KO -
50 B.$.KociupKO IlyciB < X) j $, ^,...,*/ >- ee ucfleat. Torja cymecisyet dcojieua (f(oc), TaKan, mo /Vf < >;#,..., V^ ;^, (f(oo)} jnodux oc^ed. Eoaiouy B CJiyiae a) cymecisyet CL± T) TaKoe, ITO $opuyjia (II) BU - B HeKOTOpoH noamoaejih 5= ^ 7 ',( >, W*,...,V >t B cnymae (3) &HH nponsbojibhoro a^- 6 X) $opuyjia (II) BbinoJi- B H, KpOMB TOrO, nojiokhu (7 ) B cjiywae a) 7*/o.,..., a^' /, a/ ^ ^ npn 6 ^ 7 ; qae (5) J*=^a*, al,... La/^ajnpn ^^^f- (I )-(6 ) octawtch B cmie. flaiiee, Kaaauft 3Jieue npeacoiabjihet 00608 "aboflhhk" "ochobhoro" aneuehta -i, a HwenHO : / k, v-z,...,e+2, L-i.a,... (9 ) Va\CL*y ~~(.<g. (10 ) H3 (10 ) BHflHO, HTO JJIH i- i=j (p'a* &} = IV&CL*/ a* =1. (5*^ Ha iipeahaymero n pasehctba fpa*a.*=o> 3=1,2.,... } cneayei, qio $opuyaax MOKHO HHCaTB 3KBHBdJieHTHOe BHpaaeHHe (5*) H,TaKnu odpaaom, H36ejsaTt npeaakaia pasehctba. ofijiacieli ^ H 3* onpeaejimi: nocipoehmh KoneiHO pashoshaqhotl $opmyjm Budepew eme +4» KOTOphlK BbUCJIHeT M3 3"* e^hhctbehhhfi "nepbblg" 3316 L>1. (12 ) nocipoehhh ae pabhoshanhom $opuyjibi BJieneHTOB y g+ff n d^
Kaace cbeaehhh V S^V. 51 MOKHO GHJIO 6u H ne BiigHpaTB; BCJIH B cjieayiomea Huxe $opwyjie (71) B (6) u (7) BbisepKHyTB e?ve.+t, y*» BSHTB ^ - *3, yaajihtb B t a BUBCTO (3) BSHTL ^V^/y ^ *«A JV*^** A ; Toraa npeodpasosahhah $opuyna (Jyaei pabhoana^ha (H). npeankaia <5& sosiueii npohsbonthimw (13 ). dc ( 9', Ot* Kt, >^5,J^y/V*Z)eCTL KOHiWRKUHH $0puyjl (1 ')» (2'), no'jiyqehhhx as (1 ), (2 ) sauehofi x Ha x,*(t=e+4) a cjieaywinhx $opuyji (3) - (8), rzeou,=?uu A? V*.LL *? Ve+s u- (B HHTepnperauHH: " u, - OCHOBHOH ajiemeht") H DLL = 7uu. A Doc. *A Oz. - 7- ZX*XA y- zy *^ (5) 2>x*A ^^ y * ^"x *y *, (6) IloKaseu, HTO $opwyjia pabh03h3mha, a Taicxe KoneiHo pabhosnamia $opuy^e (E). Ilpn npeflnojioaehhii cjiyvan a), a Taioce cjiywan (5), $opuyjia (yill) BbinoJiHHua B uoaejui 5', onpe^ejiehiiott same ycjioshhuh (1 ) - (13 ). flehcibhiejibho, KBK nerko ydeswibch, npa uecto df ^5"; ^,V*, -, W*i,fl-t> *, y, y *, z) HBDC x, ^, ^, z ; a npa x*=a* ;^=/,2,... OTH npoas- HM66T UOCTOod ffioty/i.,..,^ ^,^-i, %,a/>, 'V*; Z). _ J ^, ecjia t-= 7, B cjiyqae a), " "I *>i, - B OCT8JIBHUX CJiy^aHX. IlyciB TenepB $opuyna (yffl) a): BunojiHHMa B KOHeiHOtt UOACJOI; (5): BhinojiHHwa, HO HO sunonhhwa HR B oanoft KOHeinofi uoaejih. 06o3Ha«oiu lepes 5 '= < ^ ^ > ee nphbeaehhyip uoaejib, H nycis
52 B.$.KOCTHpKO HeKOTopux xyi,--.,^^, xi.?' H jnofioro Ms $opwyji (1 ')» (2')» (3) jierico ybhfleii., ITO yflobjietbopfnonie (6*), OSHH H ie me win jnodoro oc*e J'. CyneciBy- KT $yhk^hh CKOJieua X(3c), y^jc), y*(x) TaKHe, ^^x^.-.^^^^^^^yt^^-iaah jnocux x*,? Bseaeu odosaaiehiifl : a.*- a): ^=[ai_,...>a^j> ectb nepsbih nobtopubmhacn B nocjieflobaiejibhocth (M02CHO (5): 7, mo $opwyna (II) BhinojiHHMa B (XOTH, BOSMOKHO.O:^ =<27- )i ( TaK KBK npa ^ ^ / ^ ^^r, TO onpeaeaehhn npeahkaios H V i- = t- B cjiyiae a) ; O/j./, - B OCiaJIBHHX i, -1, 2,...)t- B cayqae a), ^>=-/;2,... B cnyiae 6). BoaBiieu JoxSoe oc,~&^, ^ =&'^± H JnoOoe 2=^7 cnaiajia =/5^ HJIH o&'t+t Toraa B chjiy $opuyjm (5) SJIH roofioro c y HueKT
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B.$.KocrapKO HHTB B cjieayionee Saaaia o BUIIOJIRKUOCTH qjopuyji paapeomua HJIH jnofioro KJiacca, see $opuyjiu KOioporo ofijiasaiot OSHHM HS 1) cojepacht TOJIBKO oahouecraue 2) HMeKT npuctabky 3mVn' ; 3) HMeroT npaciabky 3m'\/t'3n' ; 4) HueioT B npeasapehhok HopMajitnoM $opue L/^i 7 J "^rrli \-/rri3 v... j ~3 m-k II M f (-si, i --. JT.) i ^» _ r/je..._«_ HHCJia t^o orpahh^ehti B aananhou KJiacce (TaKotl KJiacc CSyaei coaepxaii, TOJIBKO KOHeiRoe qncjio $opuyjit ecjui napa $opityji nphsecih K cosepmehhoa HopMajiBHOft $opue). ECJIH HCKJIBIHTI. KJiaccu $opuyn 3aV3* VB^MCFi.,..,?c)» coaepsanwx ae TOJIBKO npeankaru, rae Q,, &, c - orpahhiehh B aahhow KJiacce, CL^-O, 6, c >o (nackojitko HssecTHo asiopy, npodjieiia paspeihmocth JJIH T3KUX KJiaCCOB 616 H6 peffl6ha), TO JII06ofl H3 OCTaBOHXCH KJiaCCOB $opwyji B npeasapehhor HOpuajiBHott $opue, TaKofi, qio ero $opuyjm He yflobjietbophmt ycjiobhhu I) - 4), a Ha Jmpo He HaKJiaauBaeiCH HHKa- KHX ApyriQC yc^obhft, HBJIH6TCH KJiaCCOU CB6A6HHfl. fleflctbhtejibho, 3TO BH^HO H3 paccmoipehhfl cjieayknyoc cjiyqaes (dndjmorpa$hx> cu. B[I] R [2] ) İ. KBaHTOpu V He pasaejiehh HH OAHIOI KsaHTOpoM 3 : I. 2. t/'j/ ri^j-) ( - KJiaccH 3. II. KsaHTOpu I/ passejiean KBaHiopaiiH 5. 6. 3n'\/EVM(3:) 7. - KJiaccH 3 - TpyxMecTHnfl npeahkai, Jtofioft apyrofl paccuatphbaennfl Haun idacc, KOiopua ae I) - ^), nojiyqaeich, oqebhaho, HS oflhoro H3 oaccos 1-7 KsaHiopoB HJIH npeamcatob mra saiieaofi coaepjtaipxcs B $opuynax npeahkaiob npe^hkatamh c fioatimi TOCJIOII ueci,.noaioiiy T6M <50Jiee HBJIH6TCH KJiaCCOM
KJKLCC CBeaeHHH V 3 V 55 ihtepaiypa 1. Syranyi, J., Hedukfcionstheorie des Entscheidungsprob - lems, Budapest, 1959* 2. KOCTHPKO B.$., K npotfjieue paspemrniocth fljih cjiyian AKKOPuaHa, Cad.uaT. x. (B