Let S = {0,1}. We can interpret a word w ? S * as the binary expansion of a non-negative integer,…

Let S = {0,1}. We can interpret a word w ? S* as the binary expansion of a non-negative integer, possibly with leading zeroes (e.g., 000101 and 101 both represent the integer 5). The empty wordrepresents the integer 0.

(a) Construct a DFA M1 that accepts L1 = {w ? S* | w represents an even integer}

and a DFA M2 that accepts L2 = {w ? S* | w represents a multiple of 3}.

(Hint: For M2, the states keep track of the integer mod 3.)

(b) Use the product construction to build a DFA that accepts L1 n L2 (which is all words that represent a multiple of 6).

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