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A Connection between the Star Problem and the Finite Power Property in Trace Monoids (Extended Abstract)

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Book cover Automata, Languages and Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

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).

See orchid.inf.tu-dresden.de/gdp/publikation.html for full papers [12,13].

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Author information

Authors and Affiliations

  1. Department of Computer Science, Institute of Software Engineering I, Dresden University of Technology, D, 01062, Dresden, Germany

    Daniel Kirsten

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  1. Daniel Kirsten
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Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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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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  • DOI: https://doi.org/10.1007/3-540-48523-6_44

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  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

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