Hello professor, good day. I had a question that I want to know in general. Is there a specific rule for choosing a string and implementing the pumping lemma on it? Because sometimes the example I choose to factorize is right and sometimes it's not right and I don't know how to choose right. I mean, sometimes my language is not regular, but the string I choose and how many steps I continue does not specify that this language is not regular, and when I see the solution of the question later, that course is not regular and I am so confused because every time my answer is different with the result.
Dear Sara, unfortunately there is no general rule for choosing the pumping lemma string, it depends on your intuition and experience.
If you have done some exercise on pumping lemma where you had hard times in choosing the string, please ask for office hours and I will be happy to discuss this with you.