Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
The Quest for Efficient Boolean Satisfiability Solvers
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
MathSAT: Tight Integration of SAT and Mathematical Decision Procedures
Journal of Automated Reasoning
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
A SAT-based decision procedure for the boolean combination of difference constraints
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
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
Model-based Theory Combination
Electronic Notes in Theoretical Computer Science (ENTCS)
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 Decision Procedures by (Model-)Equality Propagation
Electronic Notes in Theoretical Computer Science (ENTCS)
Annals of Mathematics and Artificial Intelligence
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
An interpolating decision procedure for transitive relations with uninterpreted functions
HVC'09 Proceedings of the 5th international Haifa verification conference on Hardware and software: verification and testing
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
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Many approaches for Satisfiability Modulo Theory (SMT rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory ). When is the combination of two simpler theories, the approach is typically handled by means of Nelson-Oppen's (NO) theory combination schema in which two specific -solver deduce and exchange (disjunctions of) interface equalities. In recent papers we have proposed a new approach to , called Delayed Theory Combination (Dtc). Here part or all the (possibly very expensive) task of deducing interface equalities is played by the SAT solver itself, at the potential cost of an enlargement of the boolean search space. In principle this enlargement could be up to exponential in the number of interface equalities generated. In this paper we show that this estimate was too pessimistic. We present a comparative analysis of Dtc vs. NO for SMT, which shows that, using state-of-the-art SAT-solving techniques, the amount of boolean branches performed by Dtc can be upper bounded by the number of deductions and boolean branches performed by NO on the same problem. We prove the result for different deduction capabilities of the and for both convex and non-convex theories.