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SAT-Solving the Coverability Problem for Petri Nets

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Abstract

Net unfoldings have attracted great attention as a powerful technique for combating state space explosion in model checking, and have been applied to verification of finite state systems including 1-safe (finite) Petri nets and synchronous products of finite transition systems. Given that net unfoldings represent the state space in a distributed, implicit manner the verification algorithm is necessarily a two step process: generation of the unfolding and reasoning about it. In his seminal work McMillan (K.L. McMillan, Symbolic Model Checking. Kluwer Academic Publishers, 1993) showed that deadlock detection on unfoldings of 1-safe Petri nets is NP-complete. Since the deadlock problem on Petri nets is PSPACE-hard it is generally accepted that the two step process will yield savings (in time and space) provided the unfoldings are small.

In this paper we show how unfoldings can be extended to the context of infinite-state systems. More precisely, we show how unfoldings can be constructed to represent sets of backward reachable states of unbounded Petri nets in a symbolic fashion. Furthermore, based on unfoldings, we show how to solve the coverability problem for unbounded Petri nets using a SAT-solver. Our experiments show that the use of unfoldings, in spite of the two-step process for solving coverability, has better time and space characteristics compared to a traditional reachability based implementation that considers all interleavings for solving the coverability problem.

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, P.O. Box 337, S-751 05, Uppsala, Sweden

    Parosh Aziz Abdulla & Aletta Nylén

  2. Department of Computer Science, NC State University, Raleigh, NC, 27695-7534, USA

    S. Purushothaman Iyer

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  1. Parosh Aziz Abdulla
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  2. S. Purushothaman Iyer
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  3. Aletta Nylén
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Abdulla, P.A., Iyer, S.P. & Nylén, A. SAT-Solving the Coverability Problem for Petri Nets. Formal Methods in System Design 24, 25–43 (2004). https://doi.org/10.1023/B:FORM.0000004786.30007.f8

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