I have this problem that I need to prove that the language is not regular by using pumping lemma, but no matter how much I read how to do it, I still don't understand. Could someone please help how to solve this?
Show that
L = { a^n c b^m | n, m are natural numbers and n < m}is not regular.
Choose a^p c b^2p. This string is in the language since p < 2p. Pumping any non-empty substring in the first p characters of this string up by a factor of more than p is guaranteed to cause the number of a to increase beyond the number of b. This contradicts the claim of the pumping lemma that doing that on a string in a regular language must give another string in that language. So, the language cannot have been regular.