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Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus

  • Florent Jacquemard
  • Étienne Lozes
  • Ralf Treinen
  • Jules Villard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6993)

Abstract

We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground), and where the logic does not permit to express tree relations x = f(y,z). We show that the problem is undecidable when these restrictions are relaxed. As motivation and application, we show how to translate the model-checking problem of \(\mathcal{A}\pi \mathcal{L}\), a spatial equational logic for the applied pi-calculus, to the validity of first-order formulas in term algebras with multiple congruence relations.

Keywords

Function Symbol Equational Theory Congruence Relation Critical Pair Ground Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Florent Jacquemard
    • 1
  • Étienne Lozes
    • 1
    • 3
  • Ralf Treinen
    • 2
  • Jules Villard
    • 1
    • 4
  1. 1.LSVENS Cachan, CNRS UMR 8643 and INRIAFrance
  2. 2.PPSUniversité Paris Diderot, CNRS UMR 7126France
  3. 3.MOVESRWTH AachenGermany
  4. 4.Queen Mary University of LondonUK

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