Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus
Identifieur interne : 003059 ( Istex/Curation ); précédent : 003058; suivant : 003060Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus
Auteurs : Florent Jacquemard [France] ; Étienne Lozes [France, Allemagne] ; Ralf Treinen [France] ; Jules Villard [France, Royaume-Uni]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
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.
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DOI: 10.1007/978-3-642-27375-9_10
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London</wicri:regionArea></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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. 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