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GATE | GATE-IT-2004 | Question 9
  • Last Updated : 30 Nov, 2015

Which one of the following statements is FALSE?
(A) There exist context-free languages such that all the context-free grammars generating them are ambiguous
(B) An unambiguous context free grammar always has a unique parse tree for each string of the language generated by it.
(C) Both deterministic and non-deterministic pushdown automata always accept the same set of languages
(D) A finite set of string from one alphabet is always a regular language.


Answer: (C)

Explanation:

A) For real-world programming languages, the reference CFG is often ambiguous, due to issues such as the dangling else problem. //Wikipedia

B) A string is ambiguous if it has two distinct parse trees;The grammar is unambiguous,if a string has distinct parse trees.

C) Deterministic pushdown automata can recognize all deterministic context-free languages while        nondeterministic ones can recognize all context-free languages

Therefore it’s FALSE



D)Properties of Regular Language:

  • The set of regular languages over an alphabet is closed under operations union, concatenation and Kleene star.
  • Finite languages are regular

So Answer is C

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