GATE CS 2025 Set 2 Q.24: Context-Free Grammars, Pushdown Automata and CFLs

Which ONE of the following languages is accepted by a deterministic pushdown automaton?

Any regular language.

Any context-free language.

Any language accepted by a non-deterministic pushdown automaton.

Any decidable language.

Official answer and solution

Official answer: A
From: Official GATE 2025 answer key

Solution

Use the strict inclusion $\text{Regular} \subsetneq \text{DCFL} \subsetneq \text{CFL} \subsetneq \text{Decidable}$ .

Every regular language is accepted by a deterministic finite automaton (DFA), which can be directly simulated by a deterministic pushdown automaton (DPDA) that never modifies its stack. In contrast, the class of deterministic context-free languages (DCFLs) is a proper subset of all context-free languages (for example, even-length palindromes $\{ww^R \mid w \in \{a, b\}^*\}$ is a CFL not accepted by any DPDA).

Final answer

Option (A)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 2 (CS2)
Question: 24 of 65
Section: Computer Science and Information Technology

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