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Variations on parallel explicit emptiness checks for generalized Büchi automata

  • TACAS 2015
  • Published:
International Journal on Software Tools for Technology Transfer Aims and scope Submit manuscript

Abstract

We present new parallel explicit emptiness checks for LTL model checking. Unlike existing parallel emptiness checks, these are based on a strongly connected component (SCC) enumeration and support generalized Büchi acceptance, and require no synchronization points or recomputing procedures. A salient feature of our algorithms is the use of a global union-find data structure in which multiple threads share structural information about the automaton checked. Besides these basic algorithms, we present one architectural variant isolating threads that write to the union-find, and one extension that decomposes the automaton based on the strength of its SCCs to use more optimized emptiness checks. The results from an extensive experimentation of our algorithms and their variations show encouraging performances, especially when the decomposition technique is used.

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Notes

  1. According to our definition, transitions of the automaton should be labeled by atomic propositions (line 8), but we omit this information as it is not pertinent to emptiness check algorithms.

  2. A complete proof can be found at: http://www.lrde.epita.fr/~renault/publis/TACAS15.pdf.

  3. Note that if A is unambiguous [7], we also have that , and are pairwise disjoint.

  4. For a description of our setup, including selected models, formulas, and detailed results, see http://www.lrde.epita.fr/~renault/benchs/STTT-2015/results.html.

  5. http://fmt.cs.utwente.nl/tools/ltsmin/#divine.

  6. For owcty and our algorithms, the run time includes the cost of generating the state-space, and of making the product with the property automaton, while cndfs explores a precomputed product. Although this sounds advantageous to cndfs in terms of absolute execution time, it may actually not be the case when measuring the scalability of the parallel algorithms: it is easier to obtain a good speedup if the cost of exploring the product automaton is high.

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Authors and Affiliations

  1. LRDE, EPITA, Kremlin-Bicêtre, France

    E. Renault & A. Duret-Lutz

  2. Sorbonne Universités, UPMC Univ. Paris 06, 75005, Paris, France

    F. Kordon

  3. CNRS UMR 7606, LIP6, 75005, Paris, France

    F. Kordon & D. Poitrenaud

  4. Université Paris Descartes, Paris, France

    D. Poitrenaud

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  1. E. Renault
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  2. A. Duret-Lutz
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  3. F. Kordon
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  4. D. Poitrenaud
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Correspondence to E. Renault.

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Renault, E., Duret-Lutz, A., Kordon, F. et al. Variations on parallel explicit emptiness checks for generalized Büchi automata. Int J Softw Tools Technol Transfer 19, 653–673 (2017). https://doi.org/10.1007/s10009-016-0422-5

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