Would it be possible to explain the physical significance of pumping length $p$ in pumping lemma for regular languages?
Somehow, the physical significance of pumping length $p$ in pumping lemma for regular languages escapes me.
I have explored a number of tutorials and presentations on this topic. The nearest I came to is, at some point, $p$ was assumed to be the number of states in the DFA recognizing the language. But the same presentation at some later point cautioned that $p$ is a property of the language, and not of the DFA.
When we prove a language to be not-regular, first of all, we assume it to be regular and thus having a pumping length $p$. We also assume the language to satisfy the conditions of pumping lemma. Later on, we find that the language fails to satisfy the conditions of pumping lemma and hence not a regular one.
So, such languages will not have any pumping length.
But what about regular languages? If I am given a regular language, there are many, just pick any one from this list, $10^*$, $1\Sigma^*$, $\Sigma^* 001$, would it be possible for us to point out the pumping length for that language?