GATE CS 2025 Set 2 — Question 24
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Theory of Computation → Context-Free Languages → DPDA vs NPDA
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Question
Which ONE of the following languages is accepted by a deterministic pushdown automaton?
Correct answer
(A) Any regular language.
Solution
A Deterministic Pushdown Automaton (DPDA) accepts the class of Deterministic Context-Free Languages (DCFLs).
1.Regular Languages: Every regular language is accepted by a Deterministic Finite Automaton (DFA). A DFA can be viewed as a DPDA that simply ignores its stack (or never pushes anything onto it). Since the set of Regular Languages is a subset of DCFLs (), every regular language is accepted by a DPDA. Hence, option (A) is correct.
2.Context-Free Languages (CFLs): CFLs are accepted by Non-deterministic Pushdown Automata (NPDAs). The set of DCFLs is a proper subset of CFLs (). There are context-free languages (specifically, inherently ambiguous languages and non-deterministic CFLs) that cannot be accepted by a DPDA. Hence, option (B) is incorrect.
3.Languages accepted by NPDA: This is equivalent to the set of Context-Free Languages. As stated above, not all such languages are accepted by a DPDA. Hence, option (C) is incorrect.
4.Decidable Languages: The set of decidable languages (Recursive languages) is a superset of CFLs (). There are many decidable languages (e.g., ) that are not even context-free, let alone accepted by a DPDA. Hence, option (D) is incorrect.
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