Question Detail: Speaking in terms of automata and regular languages, how would it be possible for a string repeating some $w$ twice equal a string repeating that same $w$ thrice? That is, why is the language $qquad L = {w in Sigma^ * mid ww = www}$ not empty? The only thing I can think of is $w = abab, ww = abababab, www = abababababab$, but I don’t think this is correct.
Asked By : jsan
Best Answer from StackOverflow
Question Source : http://cs.stackexchange.com/questions/9396
Answered By : vonbrand
The only way that $w w = w w w$ is that $w = epsilon$. Algebra of strings (for mathematician types, the free monoid on $Sigma$) isn’t that different from multiplication…
