Handbook of theoretical computer science (vol. B)
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
On Solving Presburger and Linear Arithmetic with SAT
FMCAD '02 Proceedings of the 4th 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
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
AI Communications - CASC
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
An incremental and layered procedure for the satisfiability of linear arithmetic logic
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
Model-based Theory Combination
Electronic Notes in Theoretical Computer Science (ENTCS)
Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
From KSAT to Delayed Theory Combination: Exploiting DPLL Outside the SAT Domain
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Combining Proof-Producing Decision Procedures
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Towards SMT Model Checking of Array-Based Systems
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Deciding array formulas with frugal axiom instantiation
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
Satisfiability Procedures for Combination of Theories Sharing Integer Offsets
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Ground Interpolation for Combined Theories
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Annals of Mathematics and Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Verifying heap-manipulating programs in an SMT framework
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Efficient interpolant generation in satisfiability modulo theories
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
Combining equational reasoning
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Sharing is caring: combination of theories
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining 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
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Building efficient decision procedures on top of SAT solvers
SFM'06 Proceedings of the 6th international conference on Formal Methods for the Design of Computer, Communication, and Software Systems
Optimization in SMT with LA(Q) cost functions
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Being careful about theory combination
Formal Methods in System Design
A modular approach to MaxSAT modulo theories
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Many approaches to deciding the satisfiability of quantifier-free formulae with respect to a background theory T-also known as Satisfiability Modulo Theory, or SMT(T)-rely on the integration between an enumerator of truth assignments and a decision procedure for conjunction of literals in T. When the background theory T is the combination T1 ∪ T2 of two simpler theories, the approach is typically instantiated by means of a theory combination schema (e.g. Nelson-Oppen, Shostak). In this paper we propose a new approach to SMT(T1 ∪ T2), where the enumerator of truth assignments is integrated with two decision procedures, one for T1 and one for T2, acting independently from each other. The key idea is to search for a truth assignment not only to the atoms occurring in the formula, but also to all the equalities between variables which are shared between the theories. This approach is simple and expressive: for instance, no modification is required to handle non-convex theories (as opposed to traditional Nelson-Oppen combinations which require a mechanism for splitting). Furthermore, it can be made practical by leveraging on state-of-the-art boolean and SMT search techniques, and on theory layering (i.e., cheaper reasoning first, and more often). We provide thorough experimental evidence to support our claims: we instantiate the framework with two decision procedures for the combinations of Equality and Uninterpreted Functions (EUF) and Linear Arithmetic (LA), both for (the convex case of) reals and for (the non-convex case of) integers; we analyze the impact of the different optimizations on a variety of test cases; and we compare the approach with state-of-the-art competitor tools, showing that our implemented tool compares positively with them, sometimes with dramatic gains in performance.