The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Dependence Analysis for Supercomputing
Dependence Analysis for Supercomputing
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities over Integers
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Cutting to the Chase solving linear integer arithmetic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Solving systems of linear inequalities by bound propagation
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Splitting on demand in SAT modulo theories
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Operations Research Letters
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This paper describes a novel decision procedure for quantifier-free linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g.Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaustive search for a model with bounds inference. These bounds are computed provided an oracle capable of finding constant positive linear combinations of affine forms. We also show how to design an efficient oracle based on the Simplex procedure. Our algorithm is proved sound, complete, and terminating and is implemented in the alt-ergo theorem prover. Experimental results are promising and show that our approach is competitive with state-of-the-art SMT solvers.