Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

[EN] Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free satisfiability in the initial algebra of an order-sorted equational theory (¿,E¿B) under two conditions: (i) E¿B has the finite variant property and B has a finitary unification algorithm; and (ii) (¿,E¿B) protects a constructor subtheory (¿,E¿¿B¿) that is OS-compact. These conditions apply to many user-definable theories, but have a main limitation: they apply well to data structures, but often do not hold for user-definable predicates on such data structures. We present a theory-generic satisfiability decision procedure, and a prototype implementation, extending variant-based satisfiability to initial algebras with user-definable predicates under fairly general conditions.Partially supported by NSF Grant CNS 14-09416, NRL under contract number N00173-17-1-G002, the EU (FEDER), Spanish MINECO project TIN2015-69175- C4-1-R and GV project PROMETEOII/2015/013. Ra´ul Guti´errez was also supported by INCIBE program “Ayudas para la excelencia de los equipos de investigaci´on avanzada en ciberseguridad”.Gutiérrez Gil, R.; Meseguer, J. (2018). Variant-Based Decidable Satisfiability in Initial Algebras with Predicates. Lecture Notes in Computer Science. 10855:306-322. https://doi.org/10.1007/978-3-319-94460-9_18S30632210855Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures. TOCL 10(1), 4 (2009)Armando, A., Ranise, S., Rusinowitch, M.: A rewriting approach to satisfiability procedures. 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Metalevel algorithms for variant satisfiability

Variant satisfiability is a theory-generic algorithm to decide quantifier-free satisfiability in an initial algebra when its corresponding theory has the finite variant property and its constructors satisfy a compactness condition. This paper: (i) gives a precise definition of several meta-level sub-algorithms needed for variant satisfiability; (ii) proves them correct; and (iii) presents a reflective implementation in Maude 2.7 of variant satisfiability using these sub-algorithms.NSF CNS 13-19109Ope

Unification modulo Lists with Reverse, Relation with Certain Word Equations

International audienceDecision procedures for various list theories have been investigated in the literature with applications to automated verification. Here we show that the unifiability problem for some list theories with a \emph{reverse} operator is NP-complete. We also give a unifiability algorithm for the case where the theories are extended with a \emph{length} operator on lists

HIV-1 Vpr-Induced Apoptosis Is Cell Cycle Dependent and Requires Bax but Not ANT

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Extending Index-Array Properties for Data Dependence Analysis

International audienc