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This paper deals with decision problems related to the star problem in trace monoids which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme (in: I. Privara et al. (Eds.), MFCS'94 Proc., Lecture Notes in Computer Science, vol. 841, Springer, Berlin, 1994, pp. 577-586), we know that the star problem is decidable in trace monoids...
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