GATE CS 2023 Set 1 — Question 14
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Theory of Computation → Finite Automata & Regular Languages → DFA to RE
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Question
Consider the Deterministic Finite-state Automaton (DFA) shown below. The DFA runs on the alphabet , and has the set of states , with being the start state and being the only final state.
Which one of the following regular expressions correctly describes the language accepted by ?
Correct answer
(C) 1(0 + 11)^
Solution
Analyzing the DFA transitions:
1.From start state , an input of '0' leads to state , which is a dead state (self-loops on 0 and 1 with no path to final state ). Thus, all accepted strings must start with '1'.
2., where is the final state.
3.From , an input of '0' stays in ().
4.From , an input of '1' goes to . From , another '1' returns to . This forms the pattern '11'.
5.From , an input of '0' leads to the dead state .
Combining these, once the initial '1' is consumed, the machine accepts any combination of '0's and '11's. The regular expression is .Continue learning with Success Tracker
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