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Unless otherwise noted, the alphabet for all questions below is assumed to be Σ (ab). Also note that all DFAs in your solutions should have one transition for each state in the DFA for each character in the alphabet. 1. (6 marks) This question tests your comfort with boundary cases of DFAs. Draw the state diagrams of DFAs recognizing each of the following languages. (a) (2 marks) L = {c) fore the empty string. (b) (2 marks) L (c) (2 marks) L = {a, by. 2. (8 marks) (a) (2 marks) Draw the state diagram for a DFA recognizing language Li-( (b) (2 marks) Draw the state diagrann for a DFA recognizing language L2-( (c) (Bonus +4) Draw the state diagram for a DFA recognizing language L r contains at least three bs). z starts with an a and contains at most one b) L1 U L2. Hint: One option is to use the construction of Theorem 1.25 in the text. (d) (4 marks) Draw the state diagram for a NFA recognizing language L LU2 3. (4 marks) Draw the state diagrarn for a DFA recognizing language L.- is any string except a and b}
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a lL2 2arb a , a, NFA Qab a b at DFA

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