Fragments de l'arithmétique dans une combinaison de procédures de décision

Diego Caminha Barbosa de Oliveira 1
1 VERIDIS - VERIfication pour les systèmes DIStribués
Inria Nancy - Grand Est, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications : UMR7503
Abstract : Formal methods in software and hardware design often generate formulas that need to be validated, either interactively or automatically. Among the automatic tools, SMT (Satisfiability Modulo Theories) solvers are particularly suitable to discharge such proof obligations, since their input language is equational logic with symbols from various useful decidable fragments such as uninterpreted symbols, linear arithmetic, and usual data-structures like arrays or lists. In this thesis, we first present an approach to combine decision procedures and propositional solvers into an SMT-solver. This approach is based not only on the exchange of deducible equalities between decision procedures, but also on the generation of model-equalities by decision procedures. This extends nicely the classical Nelson-Oppen combination procedure in a simple platform to smoothly combine convex and non-convex theories. Secondly, we present an original algorithm for the arithmetic fragment of difference logic and the details of how to implement a decision procedure based on this algorithm. Difference logic is modeled using graph theory. The deductions and consistency checks performed by the algorithm are done by looking for negative cycles and calculating shortest paths incrementally. The last part of the thesis presents an original incremental variation of the simplex method that we use to build a decision procedure for linear arithmetic. As for difference logic, we present the details of the decision procedure that make it suitable for our combination framework used by SMT-solvers. The methods and techniques described in this thesis were implemented and are available in our open-source SMT-solver veriT.
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Submitted on : Friday, May 27, 2011 - 5:28:03 PM
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Diego Caminha Barbosa de Oliveira. Fragments de l'arithmétique dans une combinaison de procédures de décision. Génie logiciel [cs.SE]. Université Nancy II, 2011. Français. ⟨tel-00578254v2⟩

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