Show that the language $\{0^n1^m0^n| m,n\in \mathbb{N}\}$ is not regular using closure properties.
I tried showing this using pumping lemma but I am stuck when it comes to closure properties. Please help me out!
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1It is a bit difficult to answer if we don't know what non-regular languages you know of. For example, you could show that $L \cap 0^10^ = {0^n10^n\mid n\geqslant 0}$ is non-regular and use closure properties of regular languages. – Nathaniel Oct 09 '22 at 19:26
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1https://cs.stackexchange.com/q/1031/755, https://en.wikipedia.org/wiki/Regular_language#Closure_properties – D.W. Oct 09 '22 at 19:29