GATE | GATE-CS-2005 | Question 54

Let Nf and Np denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let Df and Dp denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata, respectively. Which one of the following is TRUE?
(A) Df ⊂ Nf and Dp ⊂ Np
(B) Df ⊂ Nf and Dp = Np
(C) Df = Nf and Dp = Np
(D) Df = Nf and Dp ⊂ Np


Answer: (D)

Explanation: Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages. Mainly the former are used in parser design (Source: http://en.wikipedia.org/wiki/Pushdown_automaton ). Deterministic context-free languages (DCFL) are a proper subset of context-free languages.

Non-deterministic finite automata and Deterministic finite automata, both accept same set of languages as NFAs can be translated to equivalent DFAs using the subset construction algorithm.


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