D9 PHlrC T~P OTOMAT HCrU H~N DOAN NH~N
SIEU NGON NGlr CHINH QUY
BANG HUY RUAN(I)PHUNG VAN ON(2) ..,Abstract. We shall call the small possible number of states of a hyper-finite deterministic automaton, which recorgnizes the set of word L in the alphabet E, a complexity of a finite automaton of L, and denote by P (L). We have the following result:For any hyper-generating schernar C, the complexity of a finite automaton of L(C) is:
1G1d(G) + 1 ran
P(L(C)):S2 2
+1 I. D~T VAN DEKet qua ve lap sieu ngcn ngir chinh quy cho ta tHy vci m6i sieu ngon ngir chinh quy L, luon tCJnt ai m9t sieu nguCJn C ma L( C) = L, dCJng thoi tCJnt ai sieu otomat den dinh vo'i tr ang t.hai t5i thi~u khong qua 2 1G1 doan nh%n L(C) [goi la d9 phirc t ap otomat hiru h an do an nh%n C, ky hi~u la P(L)) [I]. M~t khac lap sieu ngon ngir chinh quy dong vOi phep hop, tich ghep, sieu l~p, giao va phep lay phan bii. Dieu do eo nghia la eo thg nh Sn diro'c m9t sieu ngon ngii: chinh quy bhg m9t so hiru han Hin cac phep tfnh: phep ho p, tich ghep, sieu l~p, giao va. phep lay phan bu tren m9t so hiru han cac sieu ngon ngir chinh quy, va. no duce goi la. sieu ngon ngir chinh quy suy r9ng. Van de d~t ra la. v&i m9t sieu ngon ngii' chinh quy suy r9ng tuy Y thl d9 phirc t ap doan nhan no se nhir the n ao. Bai nay nh~m giai quyet van de do.
SIEU NGUONM9t dCJthi dinh hiro'ng hfru han C tren bang chir cai E, eo m9t dinh kh6i dau 1/, met t%p cac dinh ket {1/1' 1/2, ... , I/n} va tren m6i canh ducc ghi m9t tu' r6ng [ky hi~u la. e, goi la. cung r6ng) ho~c mdt chir cai a cii a bang chir cai E [goi la cung cot yeu) diro'c goi la siiu nguon tren bang chir d.i E. Dinh co it nhat m9t cung cot yeu di tOi goi la. dinh cot yeu. So dinh cot yeu cu a C du'o c kf hi~u la. ICI [4]. Sieu nguon C dtro'c goi la. ilo n. ainh neu no khong chira cung r6ng va tren hai cung kh ac nhau xufit ph at tir ciing m9t dinh phai diro'c ghi b&i hai chir khac nha . Si3u ngu~n G dU'Q'c g9i la aay at!. ntu v&i bgt ky chii' cai a nso thuQc E, tU-m~i dinh cda G pHi c6 it nUt mQt cung xua:t pUt tU-d6 c6 ghi chii' cai a.Sieu ngu~n dU',!c goi la. ilern ilink illlY ild ne'u tU-m~i dinh cila G c6 dung n cung xua:t ph at tUd6 va chung diroc ghi cac chir cai khac nhau ciia bang chir cai E.Cho hai sieu ngutn Gl va G2 khOng co dlnh chung. Ta xet m9t s5 cac phep tinh sau:1. Phep hen> hai sieu ngudn: Cho hai sieu ngutn Gl va G2• Ta xay dung sieu ngutn G nhir sau: T~p dinh cila G bao gtm t~p dlnh cua Gl va G2. Ta them m9t dinh IG, la:y lam dinh vao cda G, tU-IG ta n5i hai cung r~ng t6'i hai dinh vao ciia Gl va G2. T~p dinh ke't ciia G bao gtm ta:t ca cac dinh ket cda Gl va G2. Sieu ngubn G diroc goi la hop cua sieu nguon Gl va G2 va xy hi~u la
la m~t siiu nguon G ma siiu ngon ngir sink bd-i G la kcrp ctla cac siiu ngon ngir sink beti Gl va G2 clong tkiri so iJ,ink cot ytu cda G b~ng t5ng so ilink cot ytu cda2. Tfch ghep cua m~t nguon v6i m~t sieu ngu()n: Cho ngutn Gl va sieu ngubn G2• Ta xay dimg sieu ngutn G nhtr sau: T~p dinh cua G bao gtm t~p dlnh ciia Gl va. G2. Dinh vao cua Gl dll,!C la:y lam dinh vao...
