Suppose I have a language L = {wxwR} where wR is the reverse of w, w and x has minimum length of 1, w can consist of either 0's or 1's, while x can only consist of 1's.
How do I prove that this language is not regular? Is there any other way than using the pumping lemma? If using the pumping lemma, I'm still figuring out what x,y, and z I should pick for the string s=xyz, I would appreciate if you give me any hint.
Thanks!
You should take another look into how to use the pumping lemma. You have to pick a string s, such that for each partition x,y,z, one of the pumping lemma conditions is violated.
So, let n be the "pumping-lemma-number". Pick s= 0^n 1 0^n.
From 1) you know that |xy| <= n. From 2) you know that |y|>=1. Thus y only contains 0s.
Following 3) uv^2w has also to be in L, but the first block of 0s is longer than the second one. This means 3) is violated and thus L is not regular.