Question

What is the language L(G) generated by the context-free grammar G given below?

S -> A | aB | bA | ε

A -> aS | bAA

B ->bS | aBB

Answer 1

The language accepted by given cfg is :
L(G) = {set of all strings where number of a's is greater than or equal to number of b's}
Explanation:
prodution A generates a's 1 greater than b's//consider we use S as empty string
production B generates b's 1 greater than a's
now, from S, we can call B only through S->aB, which makes, a's and b's length equal
now, from S, we can call A using A, bA,
S->bA makes a's and b's length equal
S->A makes a's greater than b's// because, in productions of A, a's are greater than B
hence overall number of a's is greater than or equal to number of b's