Question

3. (15) ALLDFA = { <D> | D is a DFA with L(D) = {*}. Show that ALLDFA E P.

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SOLUTION-

ALLDFA = {(D| D is a DFA and L(D) = Σ*).

P is a class of language which are decidable in polynomial time on DFA.

We construct a Turing machine M that decides ALLDFA in a polynomial time

    M = on input <D> where D is DFA

1. Construct DFA B that recognises L(D)' by swapping the accept and non accept states in DFA D.

2. Run the decider S of EDFA on input<B> now we can determine if this decider M runs in polynomial time.(Test weather a path exist from the satrt to each accept state in B).

3. If S accepts ,accept . If S rejects reject

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