Which ONE of the following languages is accepted by a deterministic pushdown automaton?
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- Any regular language.
- Any context-free language.
- Any language accepted by a non-deterministic pushdown automaton.
- Any decidable language.
The Correct Option is A
Solution and Explanation
- Every regular language is accepted by a DPDA since regular languages can be recognized by finite state automata, which are a subset of DPDAs. DPDAs can process regular languages in a deterministic manner, just like finite state machines.
- However, not all context-free languages (CFLs) can be accepted by a DPDA. For example, the language \( L = \{a^n b^n c^n \mid n \geq 1\} \) is context-free but cannot be recognized by any DPDA because it requires non-deterministic behavior to be accepted.
- A non-deterministic pushdown automaton (NPDA) can accept a broader class of context-free languages than a DPDA. The languages accepted by an NPDA include all deterministic context-free languages, but an NPDA can recognize languages that a DPDA cannot due to its ability to explore multiple possibilities simultaneously.
- Decidable languages include those from the Chomsky hierarchy that can be recognized by a Turing machine. However, a DPDA is strictly weaker than a Turing machine in terms of computational power, as there are languages that a DPDA cannot recognize but a Turing machine can.
Since a DPDA can accept all regular languages, the correct answer is (A) Any regular language.
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