Exercise 3. Let 2 and 2 be alphabets with 2 C \'. Let M be a DFA with alphabet 2

Question

Exercise 3. Let 2 and 2 be alphabets with 2 C '. Let M be a DFA with alphabet 2 I. Prove that there exists a DFA M, with alphabet , such that L(M,)-L(M). (Hint: add a "fail" state to M. 2. Let F be a binary operation applicable to any two formal languages. In particular, F may be applied to two languages over different alphabets. Now assume that for all alphabets and for all regular languages A and B over , F(A, B) is regular. Use Part 1 to conclude that for any two regular languages A and B (over possibly different alphabets), F(A, B) is regular.

Explanation / Answer

PDA accepts L intersection K by a final state if the transaction is defined for all states and states belongs to PDA. For each move of PDA P, we make the same move in PDA P' and also we carry also the site of DFA, A is the second component of P'. P1 accepts a string w if it is accepted by P and A

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