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Rewriting Systems over Nested Data Words

Authors Ahmed Bouajjani, Cezara Drăgoi, Yan Jurski, Mihaela Sighireanu



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Author Details

Ahmed Bouajjani
Cezara Drăgoi
Yan Jurski
Mihaela Sighireanu

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Ahmed Bouajjani, Cezara Drăgoi, Yan Jurski, and Mihaela Sighireanu. Rewriting Systems over Nested Data Words. In Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09). Open Access Series in Informatics (OASIcs), Volume 13, pp. 70-79, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DROPS.MEMICS.2009.2356

Abstract

We propose a generic framework for reasoning about infinite state systems handling data like integers, booleans etc. and having complex control structures. We consider that configurations of such systems are represented by nested data words, i.e., words of ... words over a potentially infinite data domain. We define a logic called $\ndwl$ allowing to reason about nested data words, and we define rewriting systems called $\ndwrs$ over these nested structures. The rewriting systems are constrained by formulas in the logic specifying the rewriting positions as well as structure/data transformations. We define a fragment $\Sigma_2^*$ of $\ndwl$ with a decidable satisfiability problem. Moreover, we show that the transition relation defined by rewriting systems with $\Sigma_2^*$ constraints can be effectively defined in the same fragment. These results can be used in the automatization of verification problems such as inductive invariance checking and bounded reachability analysis. Our framework allows to reason about a wide range of concurrent systems including multithreaded programs (with procedure calls, thread creation, global/local variables over infinite data domains, locks, monitors, etc.), dynamic networks of timed systems, cache coherence/mutex/communication protocols, etc.
Keywords
  • Nested data words
  • rewriting systems
  • program verification
  • dynamic and parametrized systems
  • invariance checking

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