Question

lle la b c +p || 0 | {p} | {9} | {r} 9 || {p} {9} | {r} | 0 *r || {q} / {r} | 0 | {p}

Convert the epsilon-NFA to an NFA.

Answer 1

convert the E-NIA to NFA . tena Ans let given E-NFA N= QQ,E, 8, 9o,f} Q= {p, q,8} {={a,b,c} No={p3 auf - $03 it an Equivalent NFA without E-moves it N'=(Q!, 81, 8', wo', F') Here f' is a set of states whose E-closul contains a state of F. E-closure! It contains a set of states reacha- able from a state q on e-transitions including a state qe e-closure (P)= {P3 E-closure (m): 90,P3 E-closure (8)=98, 9,8}

5'(P, a)- E-closue ( 8 (E-closure (P), a)) - E-Closure ( 8 (P, an) i E-closweco) - {P] s'(Pib) - E-closure (s (E-closure (P), b)) - E-closure (8CP, b)) - E-closul cou = &a, P3 s'(,0) - E-closue (SCE-Closue (P), c)) - E-closme (8CP, c)) - E-closme (o) = {P, 9,8} s! (au, a) - E-closul (8CE-Closure cou), a)) = 6-closune (8(2P,913, a)) = E-closue (p, q) - 9 P, 03 si cow, b) = E-Closure (66E-Closue (ov), b)) = E-closue ( 8 (98, 073, b)) = E-Clasue ($ 2,83) - Epiwor}

8 (qu, c) : e-closuue (s (e-closuue (R) ,c)) - e-closuue ( 8 (३१,१3 , c)) - e-closue (४) - ६१, ४. 8 ( 4) - -closut(s (c-closue (8),)) -- c-closuue ((६९,,०], 4)) - E-clesuue ( ११,१७,४१) - ३१,१४] 5' ( b) = E-closuue ( S (E-clossue (s), b)) - e-closuA९ ( ( ३२.१33, b)) -- e-closuu२ (१५,४१) - ३१,२,४] ( c) - E-clesuue (SCE-closuu९ (४),c)) -e-closure ( 8 (६९,१,४१, c)) - E-closuu९ (१४ , १3) - ६१,१४.

Final WFA withoud E-moves is a, b, c _ a, b, a, b, c a, b, c, ha,b,c bạc (9) 10 a,b,c Here P id Initial state and r is Final state. In converted NFA There is no E-moves.

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