GATE CS 2025 Set 1 — Question 50
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the following deterministic finite automaton (DFA) defined over the alphabet, . Identify which of the following language(s) is/are accepted by the given DFA.
Correct answer
(C) The set of all strings ending with the pattern bab.
Solution
Read the transitions from the diagram (call the states (start), , and the accepting state , left to right):
The states remember how much of the pattern the input currently ends with: = no useful suffix, = ends in , = ends in , = ends in . From , reading leaves the suffix (go to ) and reading leaves the suffix (go to ), so the machine is in exactly when the string read so far ends with .Checking the options:
| State | on | on |
|---|---|---|
- (A) has an even number of 's but ends in , so it is rejected. False.
- (B) contains but ends in (rejected). False.
- (C) Accepted exactly when the input ends with . True.
- (D) contains but is accepted (). False.
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