Question: Over alphabet {0, 1}, consider the language L = {x | the string 01 appears an odd number of times in x}. (a) (3 marks)

Over alphabet {0, 1}, consider the language L = {x | the string 01 appears an odd number of times in x}.

(a) (3 marks) Draw a DFA M = (Q, , , q0, F) such that |Q| 4 and L(M) = L.

(b) (10 marks) For the DFA M that you drew in part (a), prove using state invariants that L(M) = L.

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