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Information Processing Letters
New results on the star problem in trace monoids
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A Connection between the Star Problem and the Finite Power Property in Trace Monoids
A Connection between the Star Problem and the Finite Power Property in Trace Monoids
Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids
Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids
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ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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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 M(Γ IΓ) and M(Δ IΔ). Assume further a recognizable language L ⊆ M(Γ IΓ)×M(Δ IΔ) such that every trace in L contains 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.