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A Graph-Theoretical Characterisation of State Separation

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SOFSEM 2017: Theory and Practice of Computer Science (SOFSEM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10139))

Abstract

Region theory, as initiated by Ehrenfeucht and Rozenberg, allows the characterisation of the class of Petri net synthesisable finite labelled transition systems. Regions are substructures of a transition system which come in two varieties: ones solving event/state separation problems, and ones solving state separation problems. Linear inequation systems can be used in order to check the solvability of these separation problems. In the present paper, the class of finite labelled transition systems in which all state separation problems are solvable shall be characterised graph-theoretically, rather than linear-algebraically.

U. Schlachter—Supported by DFG (German Research Foundation) through grant Be 1267/15-1 ARS (Algorithms for Reengineering and Synthesis).

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Notes

  1. 1.

    Note that enabledness and reachability refer to d-paths, rather than to g-paths.

  2. 2.

    This definition generalises the classic notion of a Parikh vector to g-paths.

  3. 3.

    SSP(\(s,s'\)) equals SSP(\(s',s\)), and thus, SSP(\(s,s'\)) is solvable iff SSP(\(s',s\)) is solvable.

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Acknowledgments

We would like to thank the reviewers and Harro Wimmel for their very useful comments.

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Authors and Affiliations

  1. Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Eike Best & Uli Schlachter

  2. Département d’Informatique, Université Libre de Bruxelles, Boulevard du Triomphe - C.P. 212, 1050, Bruxelles, Belgium

    Raymond Devillers

Authors
  1. Eike Best
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  2. Raymond Devillers
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  3. Uli Schlachter
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Corresponding author

Correspondence to Raymond Devillers .

Editor information

Editors and Affiliations

  1. TU Dortmund , Dortmund, Germany

    Bernhard Steffen

  2. TU Dresden , Dresden, Germany

    Christel Baier

  3. Eindhoven University of Technology , Eindhoven, The Netherlands

    Mark van den Brand

  4. Alpen Adria University Klagenfurt , Klagenfurt, Austria

    Johann Eder

  5. Lero - Irish Software Research Center , Limerick, Ireland

    Mike Hinchey

  6. Lero - Irish Software Research Center , Limerick, Ireland

    Tiziana Margaria

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Best, E., Devillers, R., Schlachter, U. (2017). A Graph-Theoretical Characterisation of State Separation. In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds) SOFSEM 2017: Theory and Practice of Computer Science. SOFSEM 2017. Lecture Notes in Computer Science(), vol 10139. Springer, Cham. https://doi.org/10.1007/978-3-319-51963-0_13

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  • DOI: https://doi.org/10.1007/978-3-319-51963-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51962-3

  • Online ISBN: 978-3-319-51963-0

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