Abstract
This paper deals with a connection between the star problem and the finite power problem in trace monoids. Both problems are decidable in trace monoids without C4 submonoid [21] but remain open in all other trace monoids.
We show a connection between these problems. Assume two disjoint trace monoids IM(Γ,IΓ) and IM(Δ,IΔ. Assume further a recognizable language L L⊆ IM(Δ,IΔ)×IM(Δ,IΔ) such that every trace in L contain at least one letter in Γ and at least one letter in Δ. Our main theorem asserts that L* is recognizable iff L has the finite power property.
This work has been supported by the postgraduate program “Specification of discrete processes by operational models and logics” of the German Research Community (Deutsche Forschungsgemeinschaft).
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Kirsten, D. (1999). A Connection between the Star Problem and the Finite Power Property in Trace Monoids (Extended Abstract). In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_44
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