GATE CS 2021 Set 1 — Question 48
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the following language.Which one of the following deterministic finite automata accepts ?
Correct answer
(D) [figure]
Solution
A minimal DFA for strings ending in tracks the longest suffix that is a prefix of . The states are (start), (suffix 0), (suffix 01) and (accepting). The transitions are:
- : ,
- : ,
- : ,
- : (the suffix becomes 0), (0111 has no useful suffix)
- (A) loops on 1 in the accepting state, so it accepts . Wrong.
- (B) loops on 0 and 1 in the accepting state, so it accepts . Wrong.
- (C) sends 1 from the accepting state to , so it accepts . Wrong.
- (D) sends 0 to and 1 to the start state, which matches the construction above.
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