I'm currently working on "regular expression" exercises in the textbook ("An Introduction to Formal Languages and Automata"), and the problem that I'm facing is, most of the time, my solution is different than the book's ones. However, I realize that they could both express the same language, but I couldn't find a way to prove it. I wonder if is there a mathematical way (like induction) to prove that the two regular expression are actually identical? Any suggestion?
Thank you,