Question

Draw the state diagram of DFAs recognizing the following languages.

a. A = {w|w starts with 0 and has odd length, or starts with 1 and has even length}

b. B = {w|w is any string except 11 and 111}

c. C = {, 0}

Example of set difference: A = {0, 01}, and B = {0, 11}. Then, A − B = {01}.

Prove that regular languages are closed under the set difference operation. That is, if A and B are regular languages, then, A − B is also a regular language.

Hint: One can prove the statement above by either (1) contradiction or (2) construction. For the proof, you may make use of the theorems that regular languages are closed under union, intersection, and complement (already discussed in class).

Answer 1

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