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Polynomial-Time Many-One reductions for Petri nets

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1346))

Abstract

We apply to Petri net theory the technique of polynomialtime many-one reductions. We study boundedness, reachability, deadlock, liveness problems and some of their variations. We derive three main results. Firstly, we highlight the power of expression of reachability which can polynomially give evidence of unboundedness. Secondly, we prove that reachability and deadlock are polynomially-time equivalent; this improves the known recursive reduction and it complements the result of Cheng and al. [4]. Moreover, we show the polynomial equivalence of liveness and t-liveness. Hence, we regroup the problems in three main classes: boundedness, reachability and liveness. Finally, we give an upper bound on the boundedness for post self-modified nets: \(2^{O(size(N)^2 *\log size(N))} \). This improves a decidability result of Valk [18].

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Authors and Affiliations

  1. LSV, CNRS URA 2236; ENS de Cachan, 61 av. du Pdt. Wilson, 94235, Cachan Cedex, France

    Catherine Dufourd & Alain Finkel

Authors
  1. Catherine Dufourd
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  2. Alain Finkel
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S. Ramesh G Sivakumar

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© 1997 Springer-Verlag Berlin Heidelberg

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Dufourd, C., Finkel, A. (1997). Polynomial-Time Many-One reductions for Petri nets. In: Ramesh, S., Sivakumar, G. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1997. Lecture Notes in Computer Science, vol 1346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058039

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  • DOI: https://doi.org/10.1007/BFb0058039

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63876-6

  • Online ISBN: 978-3-540-69659-9

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