Compact normal forms in propositional logic and integer programming formulations
Computers and Operations Research
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Symbolic timing verification of timing diagrams using Presburger formulas
DAC '97 Proceedings of the 34th annual Design Automation Conference
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Deciding Linear Inequalities by Computing Loop Residues
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)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
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 SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
RTL-Datapath Verification using Integer Linear Programming
ASP-DAC '02 Proceedings of the 2002 Asia and South Pacific Design Automation Conference
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Efficient Conflict-Based Learning in an RTL Circuit Constraint Solver
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Automatic discovery of API-level exploits
Proceedings of the 27th international conference on Software engineering
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
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Solving sparse linear constraints
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
From propositional satisfiability to satisfiability modulo theories
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Lemma learning in SMT on linear constraints
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A progressive simplifier for satisfiability modulo theories
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Program analysis using quantifier-elimination heuristics
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Automated Reasoning and Mathematics
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In this paper, we present a hybrid method for deciding problems involving integer and Boolean variables which is based on generic SAT solving techniques augmented with a) a polynomial-time ILP solver for the special class of Unit-Two-Variable-Per-Inequality (unit TVPI or UTVPI) constraints and b) an independent solver for general integer linear constraints. In our approach, we present a novel method for encoding linear constraints into the SAT solver through binary “indicator” variables. The hybrid SAT problem is subsequently solved using a SAT search procedure in close collaboration with the UTVPI solver. The UTVPI solver interacts closely with the Boolean SAT solver by passing implications and conflicting assignments. The non-UTVPI constraints are handled separately and participate in the learning scheme of the SAT solver through an innovative method based on the theory of cutting planes. Empirical evidence on software verification benchmarks is presented that demonstrates the advantages of our combined method.