GATE CS 2024 Set 2 — Question 22
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Theory of Computation → Finite Automata & Regular Languages → DFA to RE
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Question
Which one of the following regular expressions is equivalent to the language accepted by the DFA given below?
Correct answer
(A) 0^ 1(0 + 10^ 1)^
Solution
The DFA has two states. Let the start state be and the accepting state be .
Transitions:
This matches option (A).
Transitions:
1.To reach from for the first time, we must read any number of 0s followed by a 1: .
2.Once in , we can stay in by reading 0s () or by going back to and returning to . The path corresponds to reading a 1, then any number of 0s (loop at ), then a 1. So, the cycle is .
3.Therefore, from , we can loop any number of times using either or . This corresponds to .
Combining these, the total regular expression is the concatenation of the initial path and the loop:This matches option (A).
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