Cuts from proofs: a complete and practical technique for solving linear inequalities over integers
 Isil Dillig,
 Thomas Dillig,
 Alex Aiken
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We propose a novel, sound, and complete Simplexbased algorithm for solving linear inequalities over integers. Our algorithm, which can be viewed as a semantic generalization of the branchandbound technique, systematically discovers and excludes entire subspaces of the solution space containing no integer points. Our main insight is that by focusing on the defining constraints of a vertex, we can compute a proof of unsatisfiability for the intersection of the defining constraints and use this proof to systematically exclude subspaces of the feasible region with no integer points. We show experimentally that our technique significantly outperforms the top four competitors in the QFLIA category of the SMTCOMP ’08 when solving conjunctions of linear inequalities over integers.
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 Title
 Cuts from proofs: a complete and practical technique for solving linear inequalities over integers
 Journal

Formal Methods in System Design
Volume 39, Issue 3 , pp 246260
 Cover Date
 20111201
 DOI
 10.1007/s107030110127z
 Print ISSN
 09259856
 Online ISSN
 15728102
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Linear inequalities over integers
 Algorithms
 Constraint solving
 Industry Sectors
 Authors

 Isil Dillig ^{(1)}
 Thomas Dillig ^{(1)}
 Alex Aiken ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Stanford University, Gates Building, 353 Serra Mall, Stanford, CA, 94305, USA