KHOA LIN THNG I HC & VA HC VA LMo0oRegular gramarsGing VinNhm trnh byPHM VN CHUNGAutomata and Formal Language41

Trn Quang Trung1ng nh Ton2L Bch Trm3H Thnh Nguyn4 Th Nguyn5 Huy Phng6V Th Thanh Nguyt8Nguyn Th Hng Loan7Thnh Vin Nhm

I. Vn Phm Tuyn Tnh Bn Tri v Bn Phi.II. Vn Phm Tuyn Tnh Phi Sinh Ra Ngn Ng Chnh Qui.III. S Tng ng Gia Ngn Ng Chnh Qui v Vn Phm Chnh QuiNi Dung Chnh

1. nh ngha : Mot van pham G = ( V, T, S, P ) c goi la tuyen tnh phai neu tat ca nhng luat sinh co dang sau :A xBA x ma A, B V , va x T*. Mot van pham goi la tuyen tnh trai neu tat ca cac luat sinh co dang sau: A Bx, hoac A x. Van pham chnh qui la van pham tuyen tnh trai hoac la tuyen tnh phai.

I. VN PHM TUYN TNH BN TRI V PHI.

2. V D : Cho cac van pham sau :G1 = ( {S}, {a, b}, S, P1) vi P1 c cho nh sau: S abS | aG2 = ( {S, S1, S2}, {a, b}, S, P2 ) vi nhng luat sinh nh sau:S S1ab,S1 S1ab | S2,S2 a,G3= ( {S, A, B}, {a, b}, S, P ) vi nhng luat sinh nh sau:S A,A aB| B Ab,Xac nh loai van pham tren cua G1,G2 va G3 :G1 : Van pham tuyen tnh PhaiG2 : Van pham tuyen tnh Trai.G3 : Van pham khong Chnh Qui.

I. VN PHM TUYN TNH BN TRI V PHI.

1. nh Ly 3.3 : Cho G = (V, T, S, P) la van pham tuyen tnh phai, th L(G) la mot ngon ng chnh quy. Chng minh: Th tc: GP to nfa

Input: Vn phm tuyn tnh-phi GP = (V, T, S, P)Output: nfa M = (Q, , , q0, F)

II. VPTTPHI SINH RA NGN NG CHNH QUY.

B1. ng vi mi bin Vi ca vn phm ta xy dng mt trng thi mang nhn Vi cho nfa Tc l: Q V.

B2. ng vi bin khi u V0, trng thi V0 ca nfa s tr thnh trng thi khi u, Tc l: S = V0

B3. Nu trong vn phm c mt lut sinh no dng Vi a1a2am Thm vo nfa mt v ch mt trng thi kt thc Vf

B4. ng vi mi lut sinh ca vn phm c dng Vi a1a2amVj Thm vo nfa cc chuyn trng thi *(Vi, a1a2am) = Vj

B5. ng vi mi lut sinh dng Vi a1a2am Thm vo nfa cc chuyn trng thi *(Vi, a1a2am) = VfII. VPTTPHI SINH RA NGN NG CHNH QUY.

II. VPTTPHI SINH RA NGN NG CHNH QUY.

V d 3.13Xay dng mot nfa chap nhan ngon ng cua van pham sau:V0 aV1 | baV1 aV1 | abV0 | bNFA ket qua

II. VPTTPHI SINH RA NGN NG CHNH QUY.

2. nh l 3.4Nu L l 1 NNCQ trn bng ch ci , th tn ti 1 VPTT phi G = ( V, , S, P) sao cho L = L(G).NFA sang VPTT: Cho M = ( Q, , , q0, F) l 1 NFA chp nhn L.Q = {q0, q1, q2, ..., qn} = {a1, a2, a3, ...., an}Chuyn sang vn phm tuyn tnh phi G = ( V, , S, P) nh sau:B1: Mi trng thi trong dfa tr thnh bin trong vn phm, V = Q, S = q0B2: Vi mi chuyn trng thi (qi, aj) = qk ca M ta xy dng lut sinh TT phi tng ngqi ajqk.B3: i vi mi trng thi qf F chng ta xy dng lut sinh qf .

II. VPTTPHI SINH RA NGN NG CHNH QUY.

V d: Xy dng VPTT phi cho ngn ng L(aab*a)Vi ngn ng, tao c s nfa nh sau

Chuyn i lut sinh, ta c lut sinh sauG : q0 aq1 q1 aq2 q2 aqf | bq2 qf Theo nh l 3.4, ta tm c kt qu. Chui aaba c th c sinh ra bi vn phmq0 aq1 aaq2 aabq2 aabaqf aaba

1. nh l 1:Mt ngn ng la chnh qui nu v ch nu tn ti mt vn phm tuyn tnh tri sao cho :L=L(r)2. nh L 2: Mt ngn ng la chnh qui nu v ch nu tn ti mt vn phm chnh qui G sao cho :L=L(G)

Kt Lun : T nh l 1 v nh l 2 ta c :L(r) L(G)

III. S TNG NG GiA NGN NG V VN PHM CHNH QUY

III. BI TP

Cu 1: Xy dng dfa chp nhn ngn ng sinh ra bi vn phmS -> abAA-> baBB-> aA | bb

Gii : abbaaSbbBA

III. BI TP

Cu 2: Xy dng vn phm tuyn tnh tri v tuyn tnh phi cho ngn ng sau:L= { anbm : n>= 2, m>=3 }Gii : SaabbbAB

ab Vn phm tuyn tnh phi:S -> aaAA -> aA | bbbBB -> bB | Vn phm tuyn tnh tri:S -> AaaA -> Aa | BbbbB -> Bb |

III. BI TP

Cu 3: Tm vn phm chnh qui cho ngn ng trn {a,b}L={ w: na(w) v nb(w) u chn }

Gii : S -> aaAA-> aaA | bbBB -> bbB | SaabbAbbaaB

The end !!!*O*O*o*o*o*o*o*o*o*o*o*Cm n thy v cc bn Lng Nghe *o*o*o*o*o*o*o*o*o*o*o*o*o*O*O*O*O