Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids

D. Kirsten, G. Richomme
2001 Theory of Computing Systems  
In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the interest of the nite power property to achieve partial solutions of this problem. We prove that the star problem is decidable in some trace monoid if and only if in the same monoid, it is decidable whether a recognizable language has the nite power property. Intermediary results allow us to give a shorter proof for the decidability of the
more » ... wo previous problems in every trace monoid without C4-submonoid. We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the nite power property, e.g., we show the decidability of these problems for recognizable languages which contain at most one non-connected trace.
doi:10.1007/s00224-001-0006-x fatcat:5grot4tre5g2hhs26mcr4cirje