MINOS(IIS): infeasibility analysis using MINOS
Computers and Operations Research
Solving linear arithmetic constraints for user interface applications
Proceedings of the 10th annual ACM symposium on User interface software and technology
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
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
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Analyzing Infeasible Mixed-Integer and Integer Linear Programs
INFORMS Journal on Computing
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
DAG-aware circuit compression for formal verification
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
A scalable method for solving satisfiability of integer linear arithmetic logic
SAT'05 Proceedings of the 8th 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
SMT-COMP: satisfiability modulo theories competition
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
DPLL(T) with exhaustive theory propagation and its application to difference logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Efficient Term-ITE Conversion for Satisfiability Modulo Theories
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
An extension of the Davis-Putnam procedure and its application to preprocessing in SMT
Proceedings of the 7th International Workshop on Satisfiability Modulo Theories
SAT modulo the theory of linear arithmetic: exact, inexact and commercial solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Asp modulo csp: The clingcon system
Theory and Practice of Logic Programming
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The past decade has seen great improvement in Boolean Satisfiability(SAT) solvers. SAT solving is now widely used in different areas, including electronic design automation, software verification and artificial intelligence. However, many applications have non-Boolean constraints, such as linear relations and uninterpreted functions. Converting such constraints into SAT is very hard and sometimes impossible. This has given rise to a recent surge of interest in Satisfiability Modulo Theories (SMT). SMT incorporates predicates in other theories such as linear real arithmetic, into a Boolean formula. Solving an SMT problem entails either finding an assignment for all Boolean and theory specific variables in the formula that evaluates the formula to TRUE or proving that such an assignment does not exist. To solve such an SMT instance, a solver typically combines SAT and theory-specific solving under the Nelson-Oppen procedure framework. Fast SAT and theory-specific solvers and good integration of the two are required for efficient SMT solving. Efficient learning contributes greatly to the success of the recent SAT solvers. However, the learning technique in SMT is limited in the current literature. In this paper, we propose methods of efficient lemma learning on SMT problems with linear real/integer arithmetic constraints. We describe a static learning technique that analyzes the relationship of the linear constraints. We also discuss a conflict driven learning technique derived from infeasible sets of linear real/integer constraints. The two learning techniques can be expanded to many other theories. Our experimental results show that lemma learning can significantly improve the speed of SMT solvers.