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Quasi-optimal partial order reduction

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Abstract

A dynamic partial order reduction (DPOR) algorithm is optimal when it always explores at most one representative per Mazurkiewicz trace. Existing literature suggests that the reduction obtained by the non-optimal, state-of-the-art Source-DPOR (SDPOR) algorithm is comparable to optimal DPOR. We show the first program with \(\mathop {\mathcal {O}}(n)\) Mazurkiewicz traces where SDPOR explores \(\mathop {\mathcal {O}}(2^n)\) redundant schedules. We furthermore identify the cause of this blow-up as an NP-hard problem. Our main contribution is a new approach, called Quasi-Optimal POR, that can arbitrarily approximate an optimal exploration using a provided constant k. We present an implementation of our method in a new tool called Dpu  using specialised data structures. Experiments with Dpu, including Debian packages, show that optimality is achieved with low values of k, outperforming state-of-the-art tools.

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Notes

  1. Observe that in this case, if \(\mathop { en }(C) \subseteq D\), the execution of never reaches line 10.

  2. See https://github.com/sosy-lab/sv-benchmarks/releases/tag/svcomp17.

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Authors and Affiliations

  1. LIPN, CNRS UMR 7030, Université Sorbonne Paris Nord, Villetaneuse, France

    Camille Coti, Laure Petrucci & César Rodríguez

  2. University of Oxford, Oxford, UK

    Marcelo Sousa

  3. Diffblue Ltd, Oxford, UK

    César Rodríguez

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  1. Camille Coti
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  2. Laure Petrucci
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  3. César Rodríguez
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  4. Marcelo Sousa
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Correspondence to Laure Petrucci.

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An independently and concurrently discovered example program with the same characteristics is presented in [4]

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Coti, C., Petrucci, L., Rodríguez, C. et al. Quasi-optimal partial order reduction. Form Methods Syst Des 57, 3–33 (2021). https://doi.org/10.1007/s10703-020-00350-4

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