Abstract
We adress in this paper the decidability of the Star Problem in trace manoids: Let L be a recognizable trace language, is L ∗ recognizable? We prove that this problem is decidable when the trace monoid is a direct product of free monoids A ∗ × {b} ∗ . This result shows, for the first time and contrary to a possible intuition, that the Star Problem is of distinct nature than the Recognizability Problem: Let L be a rational trace language, is L recognizable?
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