Question: 1. (15 marks): Let S = {a,b}. Design (and draw a picture of) a deterministic finite automaton M = (Q,8,8,90, F) for the following language

1. (15 marks): Let S = {a,b}. Design (and draw a picture of) a deterministic finite automaton M = (Q,8,8,90, F) for the following language L CE*, and explain (briefly) why your DFA is correct: L={weL* | w includes two or more a's but at most one b}. Your answer should include a brief description of each set Sq= = {we * | ** (90,w) =9} for each state qe Q in your DFA written in clear, simple English - that can help a reader to understand why your DFA really does accept the above language L. It should also include a short description of how it is possible to check that this DFA really does accept this language
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