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Parameterized verification through view abstraction

  • PV 2014
  • Published:
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Abstract

We present a simple and efficient framework for automatic verification of systems with a parametric number of communicating processes. The processes may be organized in various topologies such as words, multisets, rings, or trees. Our method needs to inspect only a small number of processes in order to show correctness of the whole system. It relies on an abstraction function that views the system from the perspective of a fixed number of processes. The abstraction is used during the verification procedure in order to dynamically detect cut-off points beyond which the search of the state space need not continue. We show that the method is complete for a large class of well quasi-ordered systems including Petri nets. Our experimentation on a variety of benchmarks demonstrate that the method is highly efficient and that it works well even for classes of systems with undecidable verification problems. In particular, the method handles the fine-grained and full version of Szymanski’s mutual exclusion protocol, whose correctness, to the best of our knowledge, has not been proven automatically by any other existing methods.

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Notes

  1. Recall that we consider here transitions that do not change the size of a configuration.

  2. In fact, the post-image is rather implemented in a similar manner than the symbolic post-image described in Sect. 4.2.1.

  3. In the case processes do not loop in-order, \(\checkmark \) is replaced with a binary relation \(R\subseteq \llbracket {1}{,}{n}\rrbracket \times \llbracket {1}{,}{n}\rrbracket \) on positions, initially empty. When process i inspects process j, the pair (i, j) is added to the relation. We say that i ticks j. This can be implemented with a matrix of size \(n{\times }n\) of boolean values and allows us to cover the case where processes inspect each other in a random order.

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Authors and Affiliations

  1. Uppsala University, Uppsala, Sweden

    Parosh Abdulla & Frédéric Haziza

  2. Brno University of Technology, Brno, Czech Republic

    Lukáš Holík

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  1. Parosh Abdulla
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  2. Frédéric Haziza
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  3. Lukáš Holík
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Correspondence to Frédéric Haziza.

Additional information

P. Abdulla and F. Haziza: supported in part by the Uppsala Programming for Multicore Architectures Research Center (UPMARC). L. Holík: supported by the Czech Science Foundation (project 13-37876P).

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Abdulla, P., Haziza, F. & Holík, L. Parameterized verification through view abstraction. Int J Softw Tools Technol Transfer 18, 495–516 (2016). https://doi.org/10.1007/s10009-015-0406-x

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