Which of the following language is accepted by a Deterministic Pushdown Automata?

Difference Between DPDA and NPDA

L(DFA) = L(NFA) ⊂ L(DPDA) ⊂ L(NPDA) ⊂ L(LBA) ⊂ L(TM)

• Regular languages [RLs] are accepted by DFA, NFA, DPDA, NPDA, LBA and TM.
• Deterministic context-free languages [DCFLs] are accepted by DPDA, NPDA, LBA and TM. Some DCFLs are not accepted by DFA and NFA.
• Context-free languages [CFLs] are accepted by NPDA, LBA and TM. Some CFLs are not accepted by DFA, NFA and DPDA.
• Context-sensitive languages [CSLs] are accepted by LBA and TM. Some CSLs are not accepted by DFA, NFA, DPDA and NPDA.
• Recursively enumerable languages are accepted by TM. Some RE languages are not accepted by DFA, NFA, DPDA, NPDA and LBA.

• Option A: Any regular language. --> Correct ✓
  • RLs are accepted by DPDA.
• Option B: Any context free language. --> Wrong ✘
  • Not all CFLs are accepted by DPDA; only DCFLs are accepted by DPDA.
• Option C: Any language accepted by a non-deterministic pushdown automaton. --> Wrong ✘
  • NPDA accepts CFLs, but all CFLs are not accepted by DPDA.
• Option D: Any decidable language. --> Wrong ✘
  • DPDA accepts only deterministic context-free languages, not all decidable languages.