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Rewriting Logic and Probabilities

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Rewriting Techniques and Applications (RTA 2003)

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Abstract

Rewriting Logic has shown to provide a general and elegant framework for unifying a wide variety of models, including concurrency models and deduction systems. In order to extend the modeling capabilities of rule based languages, it is natural to consider that the firing of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. In this paper, we discuss whether there exists a notion of probabilistic rewrite system with an associated notion of probabilistic rewriting logic.

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References

  1. Martín Abadi and Joseph Y. Halpern. Decidability and expressiveness for first-order logics of probability. Information and Computation, 112(1):1–36, July 1994.

    Article  MATH  MathSciNet  Google Scholar 

  2. Franz Baader and Tobias Nipkow. Term Rewriting and all That. Cambridge University Press, 1998.

    Google Scholar 

  3. F. Bacchus. Representing and reasoning with probabilistic knowledge. MIT-Press, 1990.

    Google Scholar 

  4. Gianfranco Balbo. Introduction to stochastic Petri nets. Lecture Notes in Computer Science, 2090:84, 2001.

    Google Scholar 

  5. Benveniste, Levy, Fabre, and Le Guernic. A calculus of stochastic systems for the specification, simulation, and hidden state estimation of mixed stochastic/nonstochastic systems. TCS: Theoretical Computer Science, 152, 1995.

    Google Scholar 

  6. A. Bergstra and J.V. Tucker. A characterisation of computable data types by means of a finite equational specification method. In Springer Verlag, editor, Automata Languages and Programming, Seventh Colloquium, Lecture Notes in Computer Science, pages 76–90, 1980.

    Google Scholar 

  7. P. Borovanský, C. Kirchner, H. Kirchner, P.-E. Moreau, and Ch. Ringeissen. An Overview of ELAN. In C. Kirchner and H. Kirchner, editors, Second Workshop on Rewriting Logic and its Applications WRLA’98, volume 15 of Electronic Notes in Theoretical Computer Science, Pont-à-Mousson (France), 1998. Elsevier Science B. V. URL: http://www.elsevier.nl/locate/entcs/volume15.html.

  8. Olivier Bournez and Claude Kirchner. Probabilistic rewrite strategies: Applications to ELAN. In Sophie Tison, editor, Rewriting Techniques and Applications, volume 2378 of Lecture Notes in Computer Science, pages 252–266. Springer-Verlag, July 22–24 2002.

    Chapter  Google Scholar 

  9. Pierre Brémaud. Markov Chains. Springer, 1991.

    Google Scholar 

  10. C. Castro. Solving Binary CSP using Computational Systems. In J. Meseguer, editor, Proceedings of 1st International Workshop on Rewriting Logic, volume 4, Asilomar (CA, USA), September 1996. Electronic Notes in Theoretical Computer Science.

    Google Scholar 

  11. M. Clavel, F. Durán, S. Eker, J. Meseguer P. Lincoln, N. Martí-Oliet, and J.F. Quesada. Towards Maude 2.0. In 3rd International Workshop on Rewriting Logic and its Applications (WRLA’00), volume 36 of Electronic Notes in Theoretical Computer Science. Elsevier, 2000.

    Google Scholar 

  12. Pedro R. D’Argenio, Holger Hermanns, and Joost-Pieter Katoen. On generative parallel composition. In Electronic Notes In Computer Science, volume 22, 1999.

    Google Scholar 

  13. L. De Alfaro. Stochastic transition systems. Lecture Notes in Computer Science, 1466:423, 1998.

    Google Scholar 

  14. Thom Frühwirth, Alexandra Di Pierro, and Herbert Wiklicky. Toward probabilistic constraint handling rules. In Slim Abdennadher and Thom Frühwirth, editors, Proceedings of the third Workshop on Rule-Based Constraint Reasoning and Programming (RCoRP’01), Paphos, Cyprus, December 2001. Under the hospice of the International Conferences in Constraint Programming and Logic Programming.

    Google Scholar 

  15. Joseph Y. Halpern. Discourse, Interaction, and Communication, chapter A logical approach to reasoning about uncertainty: a tutorial, pages 141–55. Kluwer, 1998.

    Google Scholar 

  16. H. Hansson. Time and Probability in Formal Design of Distributed Systems. Series in Real-Time Safety Critical Systems. Elsevier, 1994.

    Google Scholar 

  17. Mathieu Hoyrup. Réécriture en présence de choix probabilistes. Master’s thesis, Ecole Normale Supérieure de Lyon, 2002.

    Google Scholar 

  18. Narciso Martí-Oliet and José Meseguer. Rewriting logic: Roadmap and bibliography. Theoretical Computer Science, 285(2):121–154, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Meseguer. Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science, 96(1):73–155, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  20. Alessandra Di Pierro and Herbert Wiklicky. An operational semantics for probabilistic concurrent constraint programming. In Proceedings of the 1998 International Conference on Computer Languages, pages 174–183. IEEE Computer Society Press, 1998.

    Google Scholar 

  21. B. Plateau and K. Atif. Stochastic automata network for modelling parallel systems. IEEE Transactions on Software Engineering, 17:1093–1108, 1991.

    Article  MathSciNet  Google Scholar 

  22. M.L. Puternam. Markov Decision Processes — Discrete Stochastic Dynamic Programming. Wiley series in probabilityand mathematical statistics. John Wiley & Sons, 1994.

    Google Scholar 

  23. R. Segala and N. Lynch. Probabilistic simulations for probabilistic processes. Lecture Notes in Computer Science, 836:481, 1994.

    Google Scholar 

  24. Rob van Glabbeek, Scott A. Smolka, Bernhard Steffen, and Chris M. N. Tofts. Reactive, generative, and stratified models of probabilistic processes. In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 130–141, Philadelphia, Pennsylvania, 4–7 June 1990. IEEE Computer Society Press.

    Google Scholar 

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Bournez, O., Hoyrup, M. (2003). Rewriting Logic and Probabilities. In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_6

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  • DOI: https://doi.org/10.1007/3-540-44881-0_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40254-1

  • Online ISBN: 978-3-540-44881-5

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