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International Colloquium on Automata, Languages, and Programming

ICALP 2001: Automata, Languages and Programming pp 591–602Cite as

The Star Problem in Trace Monoids: Reductions Beyond C4

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

Abstract

We deal with the star problem in trace monoids which means to decide whether the iteration of a recognizable trace language is recognizable. We consider trace monoids K n={a 1 b 1}* × … ×{a n b n }*. Our main theorem asserts that the star problem is decidable in a trace monoid M iff it is decidable in the biggest K n submonoid in M. Thus, future research on the star problem can focus on the trace monoids K n. The recently shown decidability equivalence between the star problem and the finite power problem [14] plays a crucial role in the paper.

Partially supported by the PhD program “Specification of discrete processes and systems of processes by operational models and logics” of the DFG.

See author’s homepage for a long version including complete proofs [13].

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Author information

Authors and Affiliations

  1. Institute of Algebra, Dresden University of Technology, D-01062, Dresden, Germany

    Daniel Kirsten

Authors
  1. Daniel Kirsten
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Kirsten, D. (2001). The Star Problem in Trace Monoids: Reductions Beyond C4. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_49

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  • DOI: https://doi.org/10.1007/3-540-48224-5_49

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

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