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Cfl is closed under intersection with regular language.

Then resultant languages will be regular or cfl ?

Let X is cfl

Y is regular language

 L=X intersection Y

Then L is what?
asked in Theory of Computation by (159 points) | 71 views
Every regular language is also a CFL.
Then resultant language will be what?
Thank you so much to clear my doubt.
"Cfl is closed under intersection with regular language." means it will always be the case any CFL with any regular language will always be regular.

But we have a statement: "CFL is not closed under complementation" does not mean it will never be a CFL, It means it MAYor MAY NOT be a CFL.

2 Answers

+1 vote
Best answer
  1. CFL intersection REG ----> CFL is closed intersection with regular language . Means
  • intersection may be regular hence it is also cfl. 
  • Intersection may be cfl .

So it always gives CFL .but not above the  CFL .

answered by Boss (22.5k points)
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Let's take an exaple

X=$a^n$$b^n$|n>=0 -CFL

Y=$a^m$$b^n$|m,n>=0 -regular

$a^nb^n\bigcap a^mb^n=a^nb^n$ ,which is CFL
answered by Loyal (5.2k points)

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