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If string s is accepted by this DFA, which of these strings cannot be suffix of s?

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If string s is accepted by this DFA, which of these strings cannot be suffix of s?

(a) 111001

(b) 111111

(c) 111000

(d) 101010

The question was posed to me in a national level competition.

My doubt stems from The NFA with n-moves to the DFA in portion Finite Automata and Regular Expression of Compiler

1 Answer

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The correct answer is (a) 111001

For explanation I would say: 111001 cannot be the suffix of any string accepted by this DFA. Suppose s=w111001. No matter what state the DFA reaches after reading w, it will go to state D after reading “111”, then go to state B after reading “00” and finally reaches state C after reading “1”.

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