A new polynomial-time algorithm for linear programming
Combinatorica
Theory of linear and integer programming
Theory of linear and integer programming
Introduction to algorithms
On the complexity of integer programming
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Negative-Cycle Detection Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Proof Generation in the Touchstone Theorem Prover
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals
Electronic Notes in Theoretical Computer Science (ENTCS)
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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 efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
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Linear arithmetic decision procedures form an important part of theorem provers for program verification. In most verification benchmarks, the linear arithmetic constraints are dominated by simple difference constraints of the form x ≤y + c. Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints. In this paper, we propose an efficient decision procedure for SLA constraints, by combining a solver for difference constraints with a solver for general linear constraints. For SLA constraints, the space and time complexity of the resulting algorithm is dominated solely by the complexity for solving the difference constraints. The decision procedure generates models for satisfiable formulas. We show how this combination can be extended to generate implied equalities. We instantiate this framework with an equality generating Simplex as the linear arithmetic solver, and present preliminary experimental evaluation of our implementation on a set of linear arithmetic benchmarks.