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
On Solving Presburger and Linear Arithmetic with SAT
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
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
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
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 theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Simulating midlet's security claims with automata modulo theory
Proceedings of the third ACM SIGPLAN workshop on Programming languages and analysis for security
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
CSIsat: Interpolation for LA+EUF
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
A write-based solver for SAT modulo the theory of arrays
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
Generalizing DPLL to Richer Logics
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Annals of Mathematics and Artificial Intelligence
Encoding RTL Constructs for MathSAT: a Preliminary Report
Electronic Notes in Theoretical Computer Science (ENTCS)
CEGAR based bounded model checking of discrete time hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Bounded model checking of analog and mixed-signal circuits using an SMT solver
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Verifying heap-manipulating programs in an SMT framework
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Satisfiability modulo theories: introduction and applications
Communications of the ACM
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
Decision procedures for SAT, SAT modulo theories and beyond. the barcelogictools
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Flexible interpolation with local proof transformations
Proceedings of the International Conference on Computer-Aided Design
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A progressive simplifier for satisfiability modulo theories
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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
FDCC: a combined approach for solving constraints over finite domains and arrays
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
From strong amalgamability to modularity of quantifier-free interpolation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Quantifier-free interpolation in combinations of equality interpolating theories
ACM Transactions on Computational Logic (TOCL)
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The problem of deciding the satisfiability of a quantifier-free formula with respect to a background theory, also known as Satisfiability Modulo Theories (SMT), is gaining increasing relevance in verification: representation capabilities beyond propositional logic allow for a natural modeling of real-world problems (e.g., pipeline and RTL circuits verification, proof obligations in software systems). In this paper, we focus on the case where the background theory is the combination T1∪T2 of two simpler theories. Many SMT procedures combine a boolean model enumeration with a decision procedure for T1∪T2, where conjunctions of literals can be decided by an integration schema such as Nelson-Oppen, via a structured exchange of interface formulae (e.g., equalities in the case of convex theories, disjunctions of equalities otherwise). We propose a new approach for SMT(T1∪T2), called Delayed Theory Combination, which does not require a decision procedure for T1∪T2, but only individual decision procedures for T1 and T2, which are directly integrated into the boolean model enumerator. This approach is much simpler and natural, allows each of the solvers to be implemented and optimized without taking into account the others, and it nicely encompasses the case of non-convex theories. We show the effectiveness of the approach by a thorough experimental comparison.