Question

I had a work for the university which basically said:

‘Demonstrates that the non-regular language L={0^n 1^n : n natural} had no infinite regular sublanguages.’

I demonstrated this by contradiction. I basically said that there is a language S which is a sublanguage of L and it is a regular language. Since the possible Regular expressions for S are 0*, 1*, (1+0)* and (0o1)*. I check each grammar and demonstrate that none of them are part of the language L.

However, how I could prove that ANY non regular context free language could not contain any regular infinite sublanguages?

I don’t want the prove per se, I just want to be pointed in the right direction.

Answer 1

L = {0^n 1^n : n natural} is non-regular context free.

M = 2*3* is infinite regular.

N = L∪M is non-regular context free. N contains M.