Question

The language of balanced paranthesis is

(a) regular

(b) non regular

(c) may be regular

(d) none of the mentioned

The question was posed to me in examination.

The above asked question is from Applications of Pumping Lemma/Pigeonhole principle topic in portion Properties of Regular Languages of Automata Theory

Answer 1

Correct option is (b) non regular

For explanation I would say: Given n, there is a string of balanced parentheses that begins with more than p left parentheses, so that y will contain entirely of left parentheses. By repeating y, we can produce a string that does not contain the same number of left and right parentheses, and so they cannot be balanced.