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.
Question Source : http://cs.stackexchange.com/questions/9396
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...
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