Proving a language is Not Regular without using Pumping Lemma?

Asked Oct 12 '19 at 00:08

Active Oct 12 '19 at 04:43

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I was wondering how one would go about proving a language is Not Regular without using the traditional pumping lemma contradiction.

$$L = \{ 1^k 0^n 1^n 0^k \mid k \geq 0, n \geq 0\}$$

I've seen a method before where you would Intersect this language with another one and show that the result is Not regular. But I'm lost on what to intersect it with.

edited Oct 12 '19 at 04:43

siracusa

asked Oct 12 '19 at 00:08

Katie Rose

Isn't that a circular problem? If you intersect with a regular language, how would you prove that the resulting language is not regular? – siracusa Oct 12 '19 at 00:37
@siracusa You already know some languages are not regular. – Yuval Filmus Oct 12 '19 at 06:33
Intersect with $0^1^$. – Yuval Filmus Oct 12 '19 at 06:34

Proving a language is Not Regular without using Pumping Lemma?

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