The Star Problem and the Finite Power Property in Trace Monoids: Reductions beyond C4

Abstract

We deal with the star problem in trace monoids which means to decide whether the iteration of a recognizable trace language is recognizable. We consider trace monoids K n ={ a 1 , b 1 }*×···×{ a n , b n }*. Our main result asserts that the star problem is decidable in some trace monoid M iff it is decidable in the biggest K n submonoid M. Consequently, future research on the star problem can focus on the trace monoids K n . We develop the main results of the paper for the finite power problem. Then, we establish the link to the star problem by applying the recently shown decidability equivalence between the star problem and the finite power problem (D. Kirsten and G. Richomme, 2001, Theory Comput. Systems 34 , 193–227).