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GATE | Quiz for Sudo GATE 2021 | Question 43

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  • Last Updated : 18 Dec, 2020
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Which of the following option(s) is/are correct?

  • (I) Union of two context-sensitive languages is context-sensitive language.
  • (II) Every nondeterministic PDA can be converted to an equivalent deterministic PDA.
  • (III) Complement of an RE language is also an RE language.
  • (IV) There are more than one minimal DFA for every regular language.

Note – This question is multiple select questions (MSQ).
(A) Statement (I) is false.
(B) Statement (II) is false.
(C) Statement (III) is false.
(D) Statement (IV) is false.


Answer: (B) (C) (D)

Explanation:

  1. Statement (I) is true. The union, intersection, concatenation of two context-sensitive languages is context-sensitive, also the Kleene plus and complement of a context-sensitive language is context-sensitive.
  2. Statement (II) is false. There are some nondeterministic PDA that can not be convert to equivalent PDA because of no mechanical algorithm.
  3. Statement (III) is false. As opposed to REC languages, RE languages are not closed under complementon which means complement of RE language need not be RE.
  4. Statement (IV) is false. There is unique minimal DFA for every regular language.

So, option (A), (B), and (D) are correct.

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