Theory of linear and integer programming
Theory of linear and integer programming
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
On Solving Presburger and Linear Arithmetic with SAT
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
MathSAT: Tight Integration of SAT and Mathematical Decision Procedures
Journal of Automated Reasoning
CAV'07 Proceedings of the 19th international conference on Computer aided verification
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
NiVER: non-increasing variable elimination resolution for preprocessing SAT instances
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Lemma learning in SMT on linear constraints
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We present a decision procedure for SMT(LRA) that works by eliminating Boolean and rational variables. The algorithm we propose (DPFM) is based on a combination of the Davis-Putnam procedure and the Fourier-Motzkin elimination. We report on preliminary experiments where DPFM is not directly used to solve the formula (as its prohibitive complexity does not make it practical), but it is instead used in a controlled manner as a simplification and preprocessing device.