Minimum pumping length

While teaching the Theory of Computation alongside Kamal Bentahar in the Fall of 2021, I noticed that one of the biggest challenges students faced was calculating the minimum pumping length of a regular language. 

This was due to them not having a set of rules to follow to get an answer, as they are used to. 

However, despite my belief that reasoning through the problem is more beneficial to students than relying on fixed rules, it became clear to me that such a set of rules actually exists. I was able to prove the following: 

This was a very simple result far away from my research topic so I didn't pursue its publication.

And it was not necessary, a couple of months later, Dassow and Jecker published "Operational complexity and pumping lemmas" in Acta Informatica, vastly improving my simple result.