ace test series

Question

someone please explain option (C) and option (D).......

 

(ANSWER IS B).

 

Comments

https://cs.stackexchange.com/questions/19151/is-the-complement-of-ww-context-free

This can help you for D

and https://gateoverflow.in/203733/complement-of-cfl for C

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1 more question ..

IF L1 IS REGULAR LANGUAGE AND L2 IS DCFL BUT NOT REGULAR THEN WHAT WILL BE (L1 INTERSECTION L2)?

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is ww^r CFL. If yes, how?

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$\Sigma^* \ \cap a^n b^n = a^n b^n$

$ab \ \cap a^n b^n = ab$

i don't know how to prove it but it will be DCFL.

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IF L1 IS REGULAR LANGUAGE AND L2 IS DCFL BUT NOT REGULAR THEN WHAT WILL BE (L1 INTERSECTION L2)?

https://math.stackexchange.com/questions/1541057/dcfl-are-closed-under-intersection-with-regular-languages

is ww^r CFL. If yes, how?

$L = \left \{ ww^r | w \in \Sigma^+ \right \}$ is a context-free language

$S \rightarrow aSa | bSb | aa | bb$

$L = \left \{ ww^r | w \in \Sigma^* \right \}$ is a context-free language

$S \rightarrow aSa | bSb | \in $

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yes it is CFL.How to draw its PDA? There is no center available.

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in option C complement of WW^r which is CFL Acceptable by NPDA . and  cfl does not closed under closed under complementation so why C is not answer

C is also CSL but Not CFL