Self Doubt

Question

Very very thankful to you if anyone solve it.

DCFL ∪ Recursive

DCFL ∪ Recursive Enumerable

Recursive ∪ Recursive Enumerable

DCFL ∩ Recursive

DCFL ∩ Recursive Enumerable

Recursive ∩ Recursive Enumerable

 

Comments

@Mk Utkarsh

Take L1 as, $a^mb^m c^n$.. DCFL

Take L2 as, $a^m b^n c^n$.. DCFL

Since L2 is a DCFL, I can call it recursive, as every DCFL is recursive.

Now the intersection of L1 and L2 will be,

$a^n b^n c^n$ (a well known CSL which is not a DCFL).

So I've shown u a counter example, and that's sufficient to say that saying the intersection will be 'always DCFL' is false.

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Lakshay Kakkar yes counter example is correct. so it must be recursive? 

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Yes.