CODEWITHSUNDEEP
computer-scienceregular-languagefinite-automatafsmformal-languages
ParaPsychic
ParaPsychic

Reputation: 107

Why is {a^nb^n | n <= 10} regular?

I understand that { an bn | n>=1 } is not regular using Pumping Lemma.

But then, how is { an bn | n<=10 } regular? I thought we couldn't store the number of a and b in an automata. And I couldn't verify it with pumping lemma too.

Upvotes: 0

Views: 1079

Answers (2)

Bharath K
Bharath K

Reputation: 1

We can design a finite state automata for the given language. Hence it is regular.

Upvotes: 0

Nikolay Handzhiyski
Nikolay Handzhiyski

Reputation: 1579

Every language that has a finite number of strings as members is regular, because you can construct a finite automaton that accepts each of these strings.

You can prove it by just constructing the automaton. It has a finite number of states and by the Myhill–Nerode theorem all of the strings this automaton accepts belong to a regular language.

Upvotes: 1

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