Some undecidability results related to the star problem in trace monoids (Extended abstract)

Abstract

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 from 1994 [18], we know that the star problem is decidable in trace monoids which do not contain a C4-submonoid. It is not known whether the star problem is decidable in C4. In this paper, we show undecidability of some related problems: Assume a trace monoid which contains a C4. Then, it is undecidable whether for two given recognizable languages K and L, we have K ⊆ L *, although we can decide K ⊆ L. Further, we can not decide recognizability of K∩L *as well as universality and recognizability of K ∪L *.