necessarily Context free ??

Question

Suppose that L is Context free and R is Regular.

• $A$)  $L – R$ is necessarily Context free
• $B$)  $R – L$ is necessarily Context free

Which of the above statement/s is/are true?

Comments

is it only $A$ ?

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Yes, and 2nd one is false for CFL and even RE but not for others.

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^yes.

A) True

B) False ( not necessarily), because CFL is not closed under complementation. R-L = R INTERSECTION L'

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if L is DCFL , then B) is also true.

As DCFL closed under complement

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@kapil u meant R-L is not R.E when L is RE right ? and true when L is recursive right ?

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If possible pease support ur answer with an example. It'll be helpful indeed. :)

Answer 1

1) It's closure property. CFL is closed under Regular difference (Even every language is closed under regular difference).

2) R-L is not any standard thing , we have to do calculations to know about this so we can't say anything.