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On Probabilistic Term Rewriting

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Functional and Logic Programming (FLOPS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10818))

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Abstract

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method—polynomial and matrix interpretations—are analyzed and shown to capture interesting and nontrivial examples when automated. We capture probabilistic computation in a novel way by means of multidistribution reduction sequences, thus accounting for both the nondeterminism in the choice of the redex and the probabilism intrinsic in firing each rule.

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Notes

  1. 1.

    The completeness claim of [5] has already been refuted in [14], but [14] also contradicts our completeness result. The counterexample there is invalid since a part of reduction steps are not counted. We thank Luis María Ferrer Fioriti for this analysis.

  2. 2.

    We are grateful to the anonymous reviewer who pointed us to this example.

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Acknowledgments

We thank the anonymous reviewers for their constructive remarks that improved the paper. Example 12 is due to one of them. We thank Luis MarĂ­a Ferrer Fioriti for the analysis of a counterexample in [14]. This work is partially supported by the ANR projects 14CE250005 ELICA and 16CE250011 REPAS, the FWF project Y757, and JST ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603).

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Authors and Affiliations

  1. Inria Sophia Antipolis, Valbonne, France

    Martin Avanzini & Ugo Dal Lago

  2. Department of Computer Science, University of Bologna, Bologna, Italy

    Ugo Dal Lago

  3. National Institute of Informatics, Tokyo, Japan

    Akihisa Yamada

Authors
  1. Martin Avanzini
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  2. Ugo Dal Lago
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  3. Akihisa Yamada
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Corresponding author

Correspondence to Martin Avanzini .

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Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    John P. Gallagher

  2. Karlsruhe University of Applied Sciences, Karlsruhe, Germany

    Martin Sulzmann

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Avanzini, M., Dal Lago, U., Yamada, A. (2018). On Probabilistic Term Rewriting. In: Gallagher, J., Sulzmann, M. (eds) Functional and Logic Programming. FLOPS 2018. Lecture Notes in Computer Science(), vol 10818. Springer, Cham. https://doi.org/10.1007/978-3-319-90686-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-90686-7_9

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