Let L be the set of all strings over {0, 1} whose lengths are at most three. Since L is regular, the pumping lemma holds for L, and thus there is a pumping length p associated with L. What is the smallest possible pumping length associated with L?
For this problem, I think minimum pumping length for this language should be 4, because if pumping length is smaller than or equal to 3, then $xy^{i}z$ may not be in the given language, because its length could be longer than 3. So, I want to prove that 4 is the minimum pumping length for the given language, but I have no idea how to prove it accurately. The explanation I wrote here is too informal, I think. Can anyone help me?