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Context free grammar is not closed under:

This question was previously asked in
UGC NET Computer Science (Paper 3) Nov 2017 Official Paper
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  1. Concatenation
  2. Complementation
  3. Kleene Star
  4. Union

Answer (Detailed Solution Below)

Option 2 : Complementation
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Detailed Solution

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Concept:

Context free languages are closed under Union, Concatenation and Kleene Closure (star)

CFLs are NOT closed under intersection and not closed under complementation

Example:

L1 = pn qn rm | m, n > 0 → CFL

L2 = pm qn rn  | m, n > 0 → CFL

L = pn qn rm ∩ pm qn rn  | m, n > 0. L = pn qn rn it is not accepted by pushdown automaton and hence it is not a CFL. and hence it is not closed under intersection.

Important Point:

Context free languages

Only Deterministic Context free languages

Closed under

  • Union
  • Concatenation
  • Kleene Closure
  • Homomorphism
  • Inverse Homomorphism
  • Reversal of language
  • Intersection with Regular language

Closed under

  • Complementation
  • Inverse Homomorphism

Not Closed under

  • Complementation
  • Intersection

Not Closed under

  • Union
  • Intersection
  • Concatenation
  • Kleene closure
  • Homomorphism
  • Reversal of language
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