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

Florent Jacquemard (1, 2) , Etienne Lozes (2, 3) , Ralf Treinen (4) , Jules Villard (5, 2)

1 DAHU - Verification in databases
2 LSV - Laboratoire Spécification et Vérification
3 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University
4 PPS - Preuves, Programmes et Systèmes
5 Queen Mary University of London - Department of Computer Science

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 Apil, a spatial equational logic for the applied pi-calculus, to the validity of first-order formulas in term algebras with multiple congruence relations.

Domaines: Logique en informatique [cs.LO]

Florent Jacquemard, Etienne Lozes, Ralf Treinen, Jules Villard. Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus. Theory of Security and Applications (TOSCA, joint workshop affiliated to ETAPS), Mar 2011, Saarbrücken, Germany. pp.166-185, ⟨10.1007/978-3-642-27375-9⟩. ⟨inria-00578896⟩