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When is the Kleene star of a finite language free?

algorithm,parsing,string-matching,formal-languages,kleene-star
I'm looking for references that give an algorithm to solve this problem: Problem: Given a finite alphabet Σ and a finite language L ⊆ Σ* , determine whether L* is a free monoid. Equivalently, the problem is to determine, given a finite set of strings, whether every concatenation of these...