Context Free Languages

Question

Is the following language context free:
The set of all strings with number of a’s equal to number of b’s and the sum of a’s and b’s to be divisible by 3.

Comments

We can use Pumping lemma here

Answer 1

Yeah it will be context free. 

1st part : Set of all strings with equal noof a's and B's is a standard CFL Language accepted by Push Down Automata. 

2nd : sum of a's and B's divisible by 3 is regular language 

And intersection of regular language and  context free language is CONTEXT FREE. 

 

Theorem : If L1 is a CFL and L2 is regular then L1 $\cap$ L2 is CFL.

 

Proof for above : https://www.cs.umd.edu/~gasarch/COURSES/452/F14/cfgreg.pdf