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Asked: 2026-05-19T10:55:21+00:00

I’m having a class on automata theory, and right now we are learning the

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I’m having a class on automata theory, and right now we are learning the pumping lemma. There is an exercise question asking us to “Design a language L such that neither L nor its complement has an infinite regular subset?” But I don’t understand the question. What is an infinite regular subset? How should I find a language that can meet this requirement?

Can anyone shed some light on this question?

Thanks!

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  1. Editorial Team

    More precisely, you need to find a language L so that there is no subset of L that is a infinite regular language and there is no subset of the complement of L that is an infinite regular language.

    Here’s an incorrect example: L = the union of a^n and a^n b^n. Since a^n is a regular language and it is a subset of L, this wouldn’t work for the answer.

    For finding a L that meets the requirements, I’ve found that these kind of questions are more like puzzles. You try some things out, check if they work or not, and try to think about why they don’t solve the problem. Eventually you get your mind around the situation and come up with a solution.

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