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An Elementary Expressively Complete Temporal Logic for Mazurkiewicz Traces

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Abstract

In contrast to the classical setting of sequences, no temporal logic has yet been identified over Mazurkiewicz traces that is equivalent to first-order logic over traces and yet admits an elementary decision procedure. In this paper, we describe a local temporal logic over traces that is expressively complete and whose satisfiability problem is in Pspace. Contrary to the situation for sequences, past modalities are essential for such a logic. A somewhat unexpected corollary is that first-order logic with three variables is expressively complete for traces.

Work done while the second author was visiting LIAFA, Université Paris 7. Partial support of CEFIPRA-IFCPAR Project 2102-1 (ACSMV) is gratefully acknowledged.

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Author information

Authors and Affiliations

  1. LIAFA, Université Paris, 7, 2, place Jussieu, F-75251, Paris Cedex 05

    Paul Gastin

  2. Chennai Mathematical Institute, 92 G N Chetty Road, Chennai, 600 017, India

    Madhavan Mukund

Authors
  1. Paul Gastin
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  2. Madhavan Mukund
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

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© 2002 Springer-Verlag Berlin Heidelberg

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Gastin, P., Mukund, M. (2002). An Elementary Expressively Complete Temporal Logic for Mazurkiewicz Traces. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_80

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  • DOI: https://doi.org/10.1007/3-540-45465-9_80

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  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

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