Using pumping lemma to prove that $L = \{ a^ib^j \mid \lvert i - j \rvert \le 2 \} $ is irregular Given the following language:
$L = \{ a^ib^j \mid \lvert i - j \rvert \le 2 \} $
I am trying to prove that it is not regular. On the one hand my intuition tells me that the language is non-regular as there is no way of tracking $a^{i's}$ and $b^{j's}$.
However, when I try to prove that it is irregular using the pumping lemma I have trouble finding which word I should use to arrive at a contradiction.
Any suggestions?
You can use the word $a^pb^p$, where $p$ is the constant promised by the pumping lemma.