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A Linear-Time Algorithm for the Orbit Problem over Cyclic Groups

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CONCUR 2014 – Concurrency Theory (CONCUR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8704))

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Abstract

The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite sequences over some finite alphabet) are in the same orbit with respect to a given finite permutation group (represented by their generators) acting on this set of configurations. It is known that the problem is in general as hard as the graph isomorphism problem, which is widely believed to be not solvable in polynomial time. In this paper, we consider the restriction of the orbit problem when the permutation group is cyclic (i.e. generated by a single permutation), an important restriction of the orbit problem. Our main result is a linear-time algorithm for this subproblem.

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Author information

Authors and Affiliations

  1. Yale-NUS College, Singapore

    Anthony Widjaja Lin

  2. Department of Mathematics and Statistics, The University of Melbourne, Australia

    Sanming Zhou

Authors
  1. Anthony Widjaja Lin
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  2. Sanming Zhou
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Paolo Baldan

  2. Department of Computer Science, University of Roma “La Sapienza”, Via Salaria, 113, 00198, Rome, Italy

    Daniele Gorla

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Lin, A.W., Zhou, S. (2014). A Linear-Time Algorithm for the Orbit Problem over Cyclic Groups. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_23

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  • DOI: https://doi.org/10.1007/978-3-662-44584-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44583-9

  • Online ISBN: 978-3-662-44584-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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