We showed using De Morgan’s law that the intersection of regular languages is regular. (a)…

We showed using De Morgan’s law that the intersection of regular languages is regular.

(a) Suppose we start with finite automata M1 and M2 and construct a finite automaton M that accepts L(M1)∩L(M2) using the constructions for the union and complement of languages accepted by finite automata. If the state set of M1 is of size n1 and the state set of M2 is of size n2, estimate the size of the state set of M.

(b) Give a more direct construction of a DFA accepting L(M1)∩L(M2) by taking the cross product of the state sets of M1 and M2. How large is the resulting machine?

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