模式识别导论奇数.pdf

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2、)()ln()Ph XP?12X?5?1122()ln(|)ln(|)ln()PP XP XP?12X?6?1221221211211(|)()(|)()P XPLLXP XPLL?10?1212()(|)/(|)lXP XP X?12?12?=?2212211211()()/()PLLPLL?()iP?L?0?13?(,)iiN m C112211(|)exp()(2(2)|TiiniP XxmCxmC?)ii?11?i?11?imiCiln22n?12?()()ijd XdX?X?()id Xij?()()ijd XdX?13?1?2ijCCI?121CI?1ln|2iC?12?12?(i

3、)yxm?13?13?()(Ti)ixmxm?TX X?2211()ln()2Tiiiid XPm mX m?Ti?14?X?X?im()()iPPj?j?14?()()ijd XdX?222()2()2ln()TiijijjPXmmmmP0?3?2?2I?2?4?2?n?3?13?2?12?TX X?1ln|2iC?11()ln()()()2Tiiid xPxmCxm?i?15?11()ln()2TTiiiid XPm C mX C m?1i?16?1m2m2?3m4m1?4?3?a?b?c?d?e?3?4?2?1?2?1m1m1?1m1?2?2m2m2m1?1m2m1m1?1?2?2m2?

4、2?2?13?3?12?X?12?M?12?1ln()ln|2iP?iCj?M?1()()TiiiQxmCxm?1?1()iiACa?,(iYxm)?11nnTijijijQY AYa YY?2nn?A?TAL L?()ijLl?221(nnTTijjij iQY L LYLYl Y?)?22?22?(1)/2n nn?2?B?1iAC?2?iiiiba?20ijijaibij?j)?1120ijiinnaaBaa?23?1(nnTijjiij iQY AYb Y Y?8?9?5?1?8?3?5?1?2?1?2?21|P Xdx?1?1?X?2?2?122|P Xdx?1?2?2111|1|P

5、 XdXP XdX?1?1?2?24?111120120211|P XdXP XdXP XP XdX0?25?1?2|P XP X1|?X?1?2?2|P XP X?1|?2?1?12|P XP X?1X2?26?4?4?21()()PP?1?20?2?0?1122|()|P XlXP X?1x?2?27?22ln|P udu?12l?122|P l?2?2?20?0?2?3?6?0?2?1?1()P?2()P?0?0?1?3?62?0?110m?210m?12CCI?C?12()lX?12CCI?1112CI?21122121122121ln|1()()()()21()()221()1102

6、2TTTTTPuP XXmXmXmXmXmmm mm mX XX?1|X?12lnX?1X?3?7?3?7?2?1?3?7?2?20?0?2X2?1?2m1m1X4?2?1?121222(|)(|)LLP XdxLLP Xdx?21112212110LL?(32)?32?11220LL?12211LL?211(|)P Xdx?122(|)P Xdx?12?1*P?1?4?12?21()()PP?1122()()PP?2()P?12?112212()()PP?1()P?1()P?1()P?2?)dx?1?21?3?1?4?()()()(|)()(|PPPP XdxPP X?2111221122?

7、2121()()()PlXP?12X?ln()ijijulX?()ln()jiPP?12CCC?!112TjXXm?1TijiijumCXmXmC?1112TTijijij?X CmmmmCmm?2?1?12()|()|ijiijjPP uPP u?X?X?3?2?ijuiju?111TT?111221122iijiijijijTTiijijijTijijijE uE X CmmmmCmmm CmmmmCmmmmCmmr?4?1?1TijijijrmmCmm?ijr?i?j?11?iju2|ijiu?2?ijuAXd?1TijAmmC?211|1TTjijTijijijijiuiACAmmCC

8、 CmmmmCmmr?5?4?5?|,2iijijijruNr?6?|,2jijiju?7?ijrNr?6?7?3?111(|)(|)()shge P hpghs?#?15?gp?13?sh1(|)0P h?$?13?1pdX?13?1?1()s#?1()s#?11(|)()she P hs?#?g?g?1(|)g1pghdh?15?gp?1(|)P h?111(|)()(|)exp()(|shggP hs epghu ssh pgh1)?#?1?16?111(|)exp()(|)exp()exp(|)gttgtP hdhu ssh pghdhu ssh pghdh?17?1?2?0?1?sh

9、t?exp()exp()shst?%?18?17?18?11exp()(|)exp()gtu sstpghdhu sst?%?%?19?21exp()(1)(|)exp()(1)tgu ss tpghdhu ss t?%?%?20?19?20?21()ln()PP?&?332211()exp()()()()PstPPP?3?(?)*+,?21?33 11 3122121()()exp(1)()()()()PPs tPPPP?(?)*+,?22?19?20?21?22?31 3112221131 32111 33121 3312()()exp()()()(|)exp()()()(|)()()ex

10、p()()()exp()gttgPPu sPPpghu sPPpghdhPPu sPPu s?%?dh-%?23?19?20?23?1?2?s?3?10?0?ssopcS?M?23?1()exp()MPstu s?0M./?/?()0du stds?()du stds?24?opcSminM?24?()u sMS?1()2u?23?3?10?-s?s100.5222?h()u s#0?()su s0?X?1m2m1C2C?Y?12,D D,I1?K?K?N-KKKNP KC1?26?K?0P K?/?/?ln0P K?/?/?26?!lnlnlnln 1KNP KCKNK?/?/?01KNK?

11、KN?2?27?27?K?!?E KNVar KN1?27?!E KNENN?2?!?2Var KN 1VarNN?2?N?3?11?95%?250?50?5020%250KN?2?20%?20%?3?11?250,20%N?2?15%?27%?95%?250?1000?0.22?3?11?95%?2312?1()P?2()P?N?11NPN?22NPN?1N1K2N2K1K2K?2N-KKK12Niii=1P KKC1iiiii?3?28?i?i?27?iKNii?2?11122KK PPN?22?2?29?5?6?5?6?mC()?4?1()()()(NTKKK)TXm XmSN mm m

12、m?7?8?1()(NTKKKSXm Xm?)?7?KKXmXmmm?B?n n5ln2BtrB?%?9?9?111lnlnln(11)(1)nnnkkkKKKBtrBn?%?5?6?(,)N m c1111()ln()ln(|)ln(|)ln(|)1ln2ln()()222NNKKKKNTKKKHPP XPNnNCXmCXmX?(?6?)*+,?7?10?2111111()()()()()()NNTTKKKKKKNTKKKdXmCXmtr CXm Xmtr CXm Xm?(?+,(?)*+,?211()()dtr C SCmm mmtr C S?(?+,?1?$?(11)?11?10?111

13、1()ln2ln222ln2lnln2222NnNHCtr C SNnNSNSNSCtr CNN?%?N?12?9?12?()ln2ln22NnNSNnHN?%?2?13?5?6?10?mC?()ln2ln22NnNSNnHN?2?5?6?mX?(,)CXN mN?14?14?6?SCN?1SCN?5?SCN?1SCN?N?N?mC()m N()C N1NX?N?m?C?()m N()C N1NX?(1m N?)(1C N?5?6?811111(1)()11NKKm NXNm NXNN?9N?15?898911111121(1)(1)(1)11()()()11()()(1)NTTKKKTNNT

14、NNC NX Xm Nm NNNC NNm N Nm NXXNNm NXNm NXN?(?+,?T?16?15?16?N?1NX?(|)(,|)(|)(|)P XP XdP XPd?:6?6?6?22?(|)P X?(|)P?6?22?(|)P X6(|)P?6?(|)P?6?321?m?i(|)iP X?C?1,NXX6?m?m?m?()XmXP X d?X?m?00(,)N m K?22?0m0Kn n5?0m0K0m?111(|)()(|)()PPPP?66?6?1(|)P?6?000211()exp21exp2TPmKd?;?=?;?;?=?;?;6?6?=22212d?1)?dd?2

15、5?11|(,XN m K?0m0K1,m K1()P?m?K?m?(|P00?1K?1,)?6?iK?1K?m?m,i1,ii?)?|(,NNN mK?6?(|)P?6?0m0K1,m K11011000()()KKKCCC KCK?10?26?110010()()mKKCXC KCm?27?26?27?25?1111(|)exp2TPXmKm?;?=?1?23?24?25?1101TTTKCK1?1?1110KKC?26?110011TTT11KmC XK?m?112?111111001000011110010000()()()()()mK KmC XC KCKKmKKCCC XC KCm

16、KKCX?27?1,m K2,m K1121100()(2)KK KCCKKCC?11111222112000()2(2)(22XXmKKmC XKKCCKCm?0)?100()NKKNKCC?28?29.?1000()()NmNKNKCmC NKCm?10?0?0?37?N 0?11NTTNkkkXXXN?0?X?4?Parzen?41?Parzen?NK?Parzen?()p6?X?X?R?()RPp X dX?1?P?()p6?R?()p6?R?V?()()Pp X dXpV?6?2?R?N?k?X?R?N?kPN?2?()Pkp 6?3?3?()pVNV 6?3?()p?6?()p6?

17、1?()RRp X dXPVdX?()p6?V?2?N?N?V?3?13?V?V?V?N?V?NV?N?NV?N?N 0?()NpX?()p6?lim0NV0?4?lim?5?()p 6?NNNk0?lim0NkNN0?6?X?p?()p6?00?V?3?13?N 0?NV?00?NkN?P?N?N?Parzen?N?3?14?a?XNk?Nk?N?N?NkNk?0NV 0?Parzen?iX?iX?X?()p6?0?iX?X?1?120u?%?()p6?()u#?111()NiiNNXXp XNVh#?7?3?14?Nh?nNNVh?N?b?21()exp22uu#?3?14?()p X?N

18、K?()p X?NK?()p X?V?3?()kp X?N?V?NK?N 0?lim0V?limNk?NV0?k()p X?NK?N0?Nlim0NNkN0?NV?4?5?6?NK?Parzen?arzen?NV?P?Parzen?NK()NpX?NKNK?()NpX?N?()p X?M?M?12,M6 66?M?(|),1,2,ip XiM?!1,NXX6?6?1()p X?2()pX?43?()p X?m?()p X()p X1()()mjjjp XC#?X?()jX()jX#?()kX#?u XXX dXjk#?A?()()()0kjkXA?()u X()1u X?()()()kkku

19、XXXA#?()kX#?()1u X?1kA?jC?()p X?()jX#?12,mC CC?()p X?()jX#?jC?()jX#?()p X()jX#?()jX#?jC?jC?jC?892()()()XRu Xp Xp XdX?0R/kC?/k?C21()()()mjjXjRu Xp XCXdX#?(?)*+,?8912()()()()0jjkXjkRu Xp XCXXdXC#?/?)*/+,?m(1()()()()()()mjjkkXXjCu XXX dXu XX p X dX#?kkC A?11111111342114427iN#?(?+,()1NiCX#)*?891223443C?

20、3226?7136C?1437.1C?2(|)p X?12212223241,6,6,40CCCC?112(|)1 1212148.4p XXXX X?12212(|)1 1213.4160p XXXX X?12()()PP?|)(|)p X12(p X?XXX X?012121212.75.8?kC2B?2B?Ni?12,(0,1)NXXXN?21iX?2B?2B2NB?2B?2B?12NXe?22210()2()200XNXNXXB?CC?CCN%?2B?2()(1 2)Nj#?D?D?2)NE(NB?2()2NDNB?122212,NNXXBB?12,XX?12212NNXXB?12,N

21、XXX?(0,)NCn n5?1NTiiiAX X?AWN C?(,)N0241()1Np ANi?C?112(1)2exp()22()0N nn nnNAtr C AAC?;?C?=CCC?7?12i?C2B?,1,2,iX iN?(,)N mCX?11,iXXN m?NiCNN?1(iSX?)()1,NTiNiXXXWNC?,NAWNC?TBAB?,TTNBABWNBCB?1122,NNAWNCAWNC?1A2A?1212,NAAWNNC?12?41?M?iNi?4?1?i?iN?,ii12ZZ?Z?X?4?1?iminliilDXZ?4?1,2,ilN?X?2?X?X?X?M?ii1Tl

22、lTl?;?()(),1,2,maxild XX ZZZlN?5?X?4?2?X?4?2?2iiii=()id X13?X?()p X?()p X?X22?1?4?2?()p X?2?1X131?N?N?0N?X?NX?X?)?0N(|)(NNP XXXX.0?X?dX?0N?X?X?0?(|)NP XX?0?X?S?(PP X)0sXS?S?1sP?N?0P?0?Ns?S?N?P0?N?S?N(1-P)Nss0(1)?0?1?X?S?N?NXX0?|)()limNNXXX(NpX.0?NX?1?M?NX?i?(|)iNPX?(|)iNPX?XN?NX?X?(|)iPX?P?*P?N?0?*M

23、P(2)1PPPM%?6?N?0?P?2*P?*?6?6?)()e X p x dX?X?X?*(|XPP?b?*(|)(|)Pe xPx1iM?15?(|)(|MibPxP?2(|)ii bPx?A?2221)(|)iii bxPx?A?22*(|)Pe x21*(|)(1)i bPe xMA%?221*(|)1 2*(|)*(|)11MPe xPe xPe xMM?212*(|)*(|)1MPe xPe xM?16?16?N?X?0221lim(|)1(|)2*(|)*(|)1MNiNiMP e xPxPe xPe xM?0?%?17?N0?17?X?22121|)()2*(|)xxPPx

24、 p x dxPe xM(*(|)()12*(|)()1MiixMPe x p x dxMPPe xp x dxM?18?xxP?18?18?%?*22*(|)(|)()0Var Pe xPe x P x d?$?*2P$*22*1MPPPM%?6?4?P?3*P*0P?1M*PM?P?P?M?4?3 N?N?N?P*P1MM?1MM?*PP?*P?M?0?M?1?NX?X?N?15?14 K?K?x?N?K?K?i?ix?NK?N?4?4?K?N?0?4?4?N0?K?K?N0?K?K?x?N?N?N0?K?K=1*PP?0?4?4 N0?15?N?N?N?151?4?5?a?1?2?2N?

25、x?(1)?N?T1m?2m?4?5?b?NNRN6?6E6?2?3?4?5?a?A?B?NT6NTE6?122()nxzdxz?19?1iii?3?3?2p?11()pnpxziii?19?Xd?iixzdxz?20?2p?1p?|Z?0P?|maxZXd|1iniixz|?19?19?max(,)xzxyyzddd%21?1?AB?CD?1?2?1?2?2?+?212xzmdmm?22?x?z?x?z?1m?2m?(),()xz?20.522xzd?,i j?1Nkr?112222()()kiikjjxxxx?N?11()()ijNNkiikjjkkxxxx?23?ix?ikix?14?2

26、ki?22?21?N?C?12,C6 66?1?jNjjxjN?6mx?j?2jjxxm?C?621jCjm?jxjx?6?24?J?x?J?J?4?10?4?10?1?2x?1x2?3?N?T?11?a?T?N?11?b?T?6?8?8?4?11?b?T?1?2?2x1x?a?31?ijdij?pqDp?pqijijDd?6?6?33?pqpqdq,pqmin?1?ijd?ijd?1?N?NN5?)()()DD(0?2?(0)D?pq?pD6?q6?6?66?rkpkqkijDdddDD?6?;CC?3?r?r?,rpq?3?,inminminrkijijijpkqkijij?6?6?6?6

27、?6?44?N1?2?29?2?24?34?WSBS?2CCjjJtrSxm?11jjjx?6?2?24?1?N?C?C?J?N?C?N?0J?2?3?J?7?2222kpkqkkrkpkqpqrkrkNNNNNDDDDNNNNNN?45?rk?2pqD?,p q?J?T2DtrStrStrS?pqrpq?46?46?pNT1pipiptrSxx?pppiN mm?ipxp?46?i,qrtrS trS211pTTripippppmxxN mm1irqNNTTpqirirrriiNTTTTTiqiqqqqpppqqqrrrDxxN mxxN m mN mmN m mN m m?T?)()TTT

28、rrrppqppqpqqqTpqpqpqN m mNNNmmNNNm mNmmm?rrpppqqqpqpqpqrmN m mN m mN N mmmmN?rrppqqN mN mN m?2222TTTrrrpppqqqpqpqN m mN m mN m mN N m m?2(TTTTpqppqqpqpqm mm mm mmmmm?)Nm?2()()()(?rN m()()/TTTT?2pqD?2()()pqTpqpqpqrN NDmmmN?m?47?pqrN NN?45?4?2?pqpqpq?()()T2Dmmmm?2222pqkrkpkqpqDDDD?2pqrrrNNN NNNN2ppqN

29、ND?()()qTpqpqrmmmmN?222kpkqkkrkpkqpqrkrkrkNNNNNDDDNNNNNN?2D?4?2?31?4?3?4?4?2D?1pq?8?4?18?b?4?18?c?4?4?19?4?8?4?18?a?4?18?d?4?18?b?a?b?c?d?4?18?NN5?N?19?K?means?ISODATA?4?K?K?J?1 K?means?K?means?K?1?K?K?i?K?K?2?i6?3?11,1,2,njxjjxjK?1?3?N?61nnjj?K?3,2,1,2,1,0,08,87,79,78,77,76,68,67,66?20?K?means?4?20

30、 1,2,jK?2?4?20?10?,?2221110?99,98,89,82x1x42 ISODATA?2?3?ISODATA?Iterative Self-Organization Data Analysis Technigues?60?1?N?N?s?c?c?s?c?s?c?s?is?c?s?c?s?c?s?s?c?K?s?c?K?2?x?ijA|jiXZXZ?iZ?jX?6?iN?K?CNCN?4?1jZx?jxjN?6?j=1?2?cN?3?5?1|jjjxjN?6cNDxZ?j=1,2,jD?jD?6?11cNjjDN D?jN?4?700?go to?1?N1c2k%?go to

31、?8?(?)o?11?(?)?i?cNk2$?go t?8?j2iijZ?5?1jjixjxN.?6?=1?9?i=1?2?.?n?j2?,cNji.?n?maxj.?10?j.cN2k%?DDj?maxs?2(jNN?+1)?2?j?jZ?jjZZ?jjZZ?jZ?ISODATA?1?n?nx?nm nA5mm nxAx5?mn?nx?mx?mx?11?1?1?1?1?1?a?2?1?y?y?(a)?1?1 (b)?1?b?2X2X1X1Xy?d?1?2l?dl2l?20M?45d?500n?45?12?a?b?k?21,()nkkkD a bab?x?!?4?!iai?K?ikaa?5?!

32、ia?i?k?!?2111,()KnkkikD xxaK?)*+,?iia(?5?ja?!?22)jikkaa?*?6?111,(1KnjiikDaaK?(?)?+,?j?!?22111111111(1)kkkkjikjikDaaKKK K?)*?+,?7?21()()KKnKKnjijijiaaaa(?7?KKKKKK22222111221121()111()2()12()1njjiikkjinKKjjiikkkkjiikkkkkKDaKKKKaa aaKKKa aaK?21111()kkkjijia aaK?11122()kjjnjKa?22()(),()()jijikkkkaaaa?ia

33、?ja?-?22221122()2()()()112jijikkkkkkDaaaaKK?8?nnKK22211()()()()2iiiikkkkkiaaaaK.F?9?k222()()()()11iikkkKKaa2kKK.F?10?10?8?22nDtrC?11?C?11?C?2?1?a?b?b?2?221kk?2?K?L?21?W?W?W?110wW?0w?nn*,*aWa bW?1?100n?1?1?2mn?%?18?12n?19,?y=Ax?y?mm nAA55?20?TA?1?1Tm nT?m?A?mm nmyAx5?(21)?Dtr Ctr ACAtrC55?1212222,TTm

34、 nnn mTm?;?CFC?(?+,+,Cm n5C?=?20mkkn?2tr110?22?1mkk?1?1?m?minDD?A?22100m mnm m?55?k?W?W?9?15?mm mmZWy5?23?mZ?24?Tm mWW5122122mTm mkkkkDtr WWw?5?(?1?+,?w?W?2D1k?1mkk1111mkkkkkw?21 1jj?12mD?25?w?7?m1kkk?1?111mmkkwjjk?122Dm1mmjj?23?:0,0,0,1010?CC?6?C?:0,1,1,11?;?CC?6?C?26x32?10111;?0C?=20001?101C?=12,m

35、 m12,C C?1?2x1x?2?1?()iP?1,2,iM?ix?i?i?iR?!TiiiRE x x?3?R?!11i?()()TiiiiiiRP w RP w E x x?4?R?R?MMC?R?xTR?1?5?12()()0.5PP?1?3?2?1?1?2?KLP?KL?R?3?2?R?KL?R?R?1?100n?1?12,n?(6)?12n?$?7?12n,?m?im?A,1,2,i1T?Tmm n5?y=Ax A?8?9?Y?m?m?10?11?()nTyx?()()1nnnjjjxyy?()njy?n?y?jjj?7?m?yAxx?12?1()TmTm?()my?10?()ny

36、?m?m?11?mjj?13?()mjxy?1()1nnjjj mxxxy?G?14?!2(11(jjkkj mk me mxE?2)()nnTnTnExExyy?;?G?GG?=?15?j?k?15?111()nnjjjj mj mj me mEy?;?0?in V ,?in*V2?121A2?0?1?2?in V,A in V,*N in V?1?2?A?G=(V,P,S)NTV?V?S,A,B ,?a,b,c NTVP?,Sabc SaAbc AbbA AcBbcc0000,bBBb aBaaA aBaa000?(1nnnxa b cn)?$?aabbcc?SaAbcabAcabBbcc

37、aBbbccaabbccIIIIInnna b c?3?2?A?0?A in V,N?in V?A?G=(,P,S)NVTVNV?S ,?a,b?P?TV,Sab SaSb00?(1nnxa bn?$)ab4?3?A,B in ,a in AaB0A0NVTV?G=(,P,S)?S ,?a,b?P?NVTVNVTV,SaA AaA A000?()|1nL Ga b n?$?AaB0A0?A0?121A2?0?12?$?K?K1?2?3?K?7?2?()|1nL Ga b n?L(G)?()|1nL Ga b n?$?7?2?1?3?1?3?1?PDL?d?0L?*?a+b?a?b?a?b?a?

38、a?b?b?C?b,d,bb,bd,db,bdb?Da0?aDbD0?b?0DDb0?0?b?a?bab?bbabb?D?G?abcbabdbabcbabdb?1SSAAACADECADbECAabECAabcDCAabcDbCAabcbDbCAabcbabCAabcbabdAIIIIIIIIIII?A?x?*SabcbabdAxAxACxACCxDECCxDbECCxbDbECCxbabECCxbabcDCCxbabcDbCCxbabcbDbCCxbabcbabCCxbabcbabdbIIIIIIIIIIIII?abcbabdbabc?babdb?S?S1?2SSBABbAebAebDEeb

39、DbEebabEebcbcDebabcbDebabcbDbebabcbabIIIIIIIIIII?A?0?1?4?1?2?%?n?G=(,P,S)?NVTV,NVS A?,TVa b c?P?b?1?2?,ScA AbA A000 a)(0ncb a n$3?1?1?G?NV*GAvAxI?v,x?1?1?G?L(G)?4?u,v,w,x,y?G?A?*,GGSuAy AvAx AwIII*G?v?x?j?z?v?*SuAyuvAxyIIjjjjuv Ax yuv wx yII?1?1?juv wyjuwx y?1?2?L?L?p?q?L?z?|z|p?z?z?uvwxy?|vwx|%q?v?

40、x?L?0j$jjuv wx y?7?5?cd?cadb?caadbb?jjuv wx y aaddCCaCb?7?5bbd?1?5?3?1?A?x?A?11223,AB BB BB000*GAI x?A?*GSA?I?A?A?1?6?Chomsky?Greibach?1?6?1 Chomsky?Chomsky?a in?A?B?C in?A0a,0bb0bBABC0TVNV?Chomsky?(,)GS Ca b cP S?P?Chomsky?Gc?,SaCbb CaCbb Cc00?A?B?SaCb0,SACBB Aa B00?Ca?Cb0CACB0,Aa Bb00?D?E?,DAC EB0

41、0BBBc?SDSACB0E0 CA?CB0CDE0?(,)CGS A B C D Ea b cP S?P?,SDE DAC EBB CDE Aa Bb C0000000?Chomsky?1?6?2 Greibach?Aa?0?in*NV?Greibach?G?Greibach?B?Greibach?2GB 0bb02P?,SaCBB CaCBB Cc B000?Greibach?1?3?G?1AB?0?P?1,.rBB00?B?P?1AB2?0?11212,.rAA?00?G?1G?ABA?1?3?A?B?1AA2?0?1,.rAA00?1?3?11212,.rAA?00?AA?0?z?1?

42、4?(,)NTGVVP S?1,.rAAAA?00?A?A?A?1,.rAA00?2(,)NTGVZVP S?P1iiAiSAZ0;%0=?1iiZirZZ?0;%0?ii1i2in?iAA?0?iA0?112ii1i2iiiiiiAZZZin?00000?Greibach?Chomsky?Chomsky?Greibach?Chomsky?x?12,nA A?iiAa0ijkAA A0?1?n?ijkAA A0?()ijsAA Y ij0?iAa0 Y41A445YA A ij?25152,AA A AA A00?i0?OhxT?()hn x?hx?(|qhp Gx)?hx?qG()qijhN

43、x?hx?iAi0?ijijikqqqknpn?2?ikqkn?qG12,iiikiAAAA10000?2?12,iiqqnn?2?112(,),(,)NTNTGVVP Q S GVVP Q S?1Q2Q SaSSaSbSSb0000111112113114pppp 211212213214pppp 11121314()AAAA0000?a?b?ab?100?a?30?aa?20?aabbb?5?bb?25?b?20?5?aabbb?1G2G?qijp?11223313234455,()30,()20,()5,(|)(|)0.5,()25,()20 xa n xxaa n xxaabbb n

44、xp Gxp Gxxbb n xxa n x?1?2?q?1?1?1111111111()(|)()nn x p Gx Nx?2121112313111341411145151115()(|)()()(|)()()(|)()()(|)()n xp Gx Nxn xp Gx Nxn xp Gx Nxn xp Gx Nx?30 1 020 1 1 5 0.5 225 0 020 0 0?25?1111()Nx1G1xa?11A0?0?SaS01112()Nx?1?11211311450,5,2.5nnn?2?111111111112113114112113114250.303255052.50.6

45、06,0.061,0.03npnnnnppp?2G211212213214,pppp?1122(,),(,),NTNTTNGVVP Q S GVVP Q S Va b VS?ab 1Q2QP?0.303 0.061 SaS0 0.606 0 S 0 0.061 0364 SbS0S 0 0.030 0.576?3?3?0(,)zfRQq F D.?O?D?3?0(,)zfRQqF D.?O?01232,Qq q q qa bFqD.?O?0013,q aq q q.?00(|,)1p qa qp?10(|,)2p qa qp?30(|,)3p qa qp?0,q bq1.?10(|,)1p q

46、 b q?22333344,SbB BbB BaB BaB Bb00000?4bB0?032ScA0?R?(,)NTGVVP S?232342222333,:,NTVS A A B B BVa b cP ScA AaA AaA Ab ScA?00000,?2233334424,SbB BbB BaB BaB Bb BbB000000?3A4B?3A4B?3A3B?2A3A(,):,GS A Ba b cP SP ScA AaA Ab SbB BbA?00000?4?2?R?R?R?2?R?caaab,bbaab,caab,bbab,cab,bbb,cb?R?1?R?caaab?112233,S

47、cA AaA AaA Aab0000?2?n?3Aa0b1nAaa0?R?2?R?n?3?4?bbaab?445566,SbA AbA AaA Aab0000?2?6Aa0b?caab?3Ab0?11223,ScA AaA AaA000?bbab?6Ab0?44556,SbA AbA AaA000?cab?2Ab0?bbb?3Ab0?cb?1Ab0?R?112233321ScAAaAAaAAabAbAbAb0000000 44556665SbAAbAAaAAabAbAb000000?12mAa a012,nmmAa AAa00nAbbb2mA12mAa a0233,AaA A002A3A3Aa

48、01122221,ScA AaA AaA Ab A00000?2A3A2AaA0R?R?11(,1),(,1),(,)(,1),(,1),h aa Rh aba Rqq bh ab Rh abb Rq q.?J?2?12(,)(,)(,)(,)q bq bqaqbq.JJ?J?0(,)fRQq F.?O?01212,Qq q q qa bFq qJ?O?7?18?a?a,b0q1q2qqJ0q1qqJabbaa,bbaabba,b?7?18(b)(a)?7?18?a?7?18?b?2q1q (,):,GS Aa bP SP SaA Sa AbA Ab?0000?ab?(0n)n$R?K?3?(

49、,fRRK?)0 fRL RR?P$fL RRR(,)fL RRK?0K$?,)K(?KR?$?K(,)?K?0?*(,)fTL RRKV?K?0?K?0?Z?TVR?K?(,)h Z RK?0?0q0q0q*TV?(,1)(,)ffL RRKL RRK?P?7?19?0LR?0L0RL?P?K?(,)fL RRK?0L?5?1.?2.?3.?4.?5?1?P7-5?nnna b c(,1)fL RR?(,1)fL RR?(,2)fL RR?R?(,)fL RRK?7?19?CAT?a?c?2NcN03(,)2?3Nd0Ga?F?c d c d(,)2?(,)2?5 (,)2?3?mSZS?1

50、?3?2?(?)?1?3?2?mSS?ZZS?mSmSS?ZmSZS?7?20?a?b?b?b?12SSll?mSS?Z?a?b?mSZS?7?20?ZmSS?dbabcbabdbabcbab?(,)NTGaVVP S?1121212,NVS Q Q R M MA B B C D?a?b?c?d?12,A B B C D?1,2M M?R?12,Q Q,TVa b c d?()xA xl?121212,xB B M MR Q Q?a?c?d?S?12()(,)SsA Sll?P?12SQQ011,SQQlll?2 2Ql?A?S?12QQl l?1QD0RR2QD01QRl l2QRll?iQ