Peter Linz Edition 5 Exercise 12.4 Question 7 (Page No. 321)

Question

Let $G_1$ be a context-free grammar and $G_2$ a regular grammar. Is the problem $L(G_1)\cap L(G_2) = \phi$ decidable$?$

Answer 1

yeah it is decidable because L(G1)intersectionL(G2) regular intersection [L(G1) context free (in worst case CFL it may be regular language also) and L(G2) is regular language]

and regular intersection is closed under that language so L(G1)INTERSECTIONL(G2) is CFL and CFL is decidable emptiness so it is DECIDABLE