Theory of linear and integer programming
Theory of linear and integer programming
Hermite normal form computation using modulo determinant arithmetic
Mathematics of Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
A course in computational algebraic number theory
A course in computational algebraic number theory
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Symbolic timing verification of timing diagrams using Presburger formulas
DAC '97 Proceedings of the 34th annual Design Automation Conference
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
RTL-Datapath Verification using Integer Linear Programming
ASP-DAC '02 Proceedings of the 2002 Asia and South Pacific Design Automation Conference
Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
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
Applications of craig interpolants in model checking
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We propose a novel, sound, and complete Simplex-based algorithm for solving linear inequalities over integers. Our algorithm, which can be viewed as a semantic generalization of the branch-and-bound 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 QF-LIA category of the SMT-COMP '08 when solving conjunctions of linear inequalities over integers.