Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Verification of clock synchronization algorithms: experiments on a combination of deductive tools
Formal Aspects of Computing
Model-based Theory Combination
Electronic Notes in Theoretical Computer Science (ENTCS)
Combining Decision Procedures by (Model-)Equality Propagation
Electronic Notes in Theoretical Computer Science (ENTCS)
veriT: An Open, Trustable and Efficient SMT-Solver
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Combining Non-stably Infinite, Non-first Order Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals
Electronic Notes in Theoretical Computer Science (ENTCS)
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Splitting on demand in SAT modulo theories
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
DPLL(T) with exhaustive theory propagation and its application to difference logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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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, as 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 paper, we present an approach to combine decision procedures and propositional solvers into an SMT-solver, 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. We show the soundness and completeness of this approach using an original abstract framework to represent and reason about SMT-solvers. We then describe an algorithmic translation of this method, implemented in the kernel of the veriT solver (Bouton et al. (2009)) [9].