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
Let's trace the DFA transitions:
- State (start): seen nothing or just 'a's.
- State : last seen 'b'.
- State : last seen 'ba'.
- State (final): last seen 'bab'.
- : (Accepted)
- : (Accepted)
- : (Not accepted)
- (A) is false: has 2 's (even) and is accepted, but has 2 's and is not accepted ().
- (B) is false: contains but is not accepted.
- (D) is false: contains and is accepted ().
- (C) is the most likely intended answer. While the DFA technically accepts strings ending in , in many competitive exam contexts, such a DFA is intended to represent strings ending in the pattern , possibly with a slight error in the diagram (the 'a' loop on the final state). Given the choices, (C) is the only plausible option.
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