Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A machine program for theorem-proving
Communications of the ACM
Bounded Model Checking for Timed Systems
FORTE '02 Proceedings of the 22nd IFIP WG 6.1 International Conference Houston on Formal Techniques for Networked and Distributed Systems
Symbolic Model Checking without BDDs
TACAS '99 Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
SAT-Based Procedures for Temporal Reasoning
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Handbook of automated reasoning
Handbook of automated reasoning
The LPSAT engine & its application to resource planning
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Applying SAT Solving in Classification of Finite Algebras
Journal of Automated Reasoning
Verifying Industrial Hybrid Systems with MathSAT
Electronic Notes in Theoretical Computer Science (ENTCS)
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
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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
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In the last years we have witnessed an impressive advance in the efficiency of boolean solving techniques, which has brought large previously intractable problems at the reach of state-of-the-art solvers. Unfortunately, simple boolean expressions are not expressive enough for representing many real-world problems, which require handling also integer or real values and operators. On the other hand, mathematical solvers, like computer-algebra systems or constraint solvers, cannot handle efficiently problems involving heavy boolean search, or do not handle them at all. In this paper we present the foundations and the basic algorithms for a new class of procedures for solving boolean combinations of mathematical propositions, which combine boolean and mathematical solvers, and we highlight the main requirements that boolean and mathematical solvers must fulfill in order to achieve the maximum benefits from their integration. Finally we show how existing systems are captured by our framework.