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

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


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.


Function Symbol Equational Theory Congruence Relation Critical Pair Ground Term 
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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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