Peter Linz Edition 4 Exercise 4.3 Question 9 (Page No. 123)

Question

Is the language $L=$ {$w∈$ {$a,b,c$}$^*$ $:|w|=3n_a(w)$} regular?

Answer 1

The given language is L= {abc,aabccc,aaabbcccc,....}

The length of the string should be thrice of the number of a's.

As we use finite automata to check whether a given language is regular or not, we cannot count the number of alphabets (length of the string due to finite memory) . So the given language L is not regular.