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Rewriting Systems with Data

A Framework for Reasoning About Systems with Unbounded Structures over Infinite Data Domains

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Fundamentals of Computation Theory (FCT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4639))

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Abstract

We introduce a uniform framework for reasoning about infinite-state systems with unbounded control structures and unbounded data domains. Our framework is based on constrained rewriting systems on words over an infinite alphabet. We consider several rewriting semantics: factor, prefix, and multiset rewriting. Constraints are expressed in a logic on such words which is parametrized by a first-order theory on the considered data domain. We show that our framework is suitable for reasoning about various classes of systems such as recursive sequential programs, multithreaded programs, parametrized and dynamic networks of processes, etc. Then, we provide generic results (1) for the decidability of the satisfiability problem of the fragment ∃ * ∀ * of this logic provided that the underlying logic on data is decidable, and (2) for proving inductive invariance and for carrying out Hoare style reasoning within this fragment. We also show that the reachability problem is decidable for a class of prefix rewriting systems with integer data.

Partially supported by the French ANR project ACI-06-SETI-001.

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Authors and Affiliations

  1. LIAFA, CNRS & U. Paris 7, Case 7014, 2 place Jussieu, 75251 Paris 05, France

    Ahmed Bouajjani, Peter Habermehl, Yan Jurski & Mihaela Sighireanu

  2. LSV, CNRS & ENS Cachan, 61 av Président Wilson, 94235 Cachan, France

    Peter Habermehl

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  1. Ahmed Bouajjani
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  2. Peter Habermehl
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  3. Yan Jurski
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  4. Mihaela Sighireanu
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Erzsébet Csuhaj-Varjú Zoltán Ésik

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Bouajjani, A., Habermehl, P., Jurski, Y., Sighireanu, M. (2007). Rewriting Systems with Data. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_1

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  • DOI: https://doi.org/10.1007/978-3-540-74240-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74239-5

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