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
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
Symbolic heap abstraction with demand-driven axiomatization of memory invariants
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
Small formulas for large programs: on-line constraint simplification in scalable static analysis
SAS'10 Proceedings of the 17th international conference on Static analysis
Precise reasoning for programs using containers
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Efficient interpolant generation in satisfiability modulo linear integer arithmetic
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Cutting to the Chase solving linear integer arithmetic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Simplifying loop invariant generation using splitter predicates
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Fluid updates: beyond strong vs. weak updates
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
A simplex-based extension of fourier-motzkin for solving linear integer arithmetic
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Minimum satisfying assignments for SMT
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
SMTInterpol: an interpolating SMT solver
SPIN'12 Proceedings of the 19th international conference on Model Checking Software
Proof tree preserving interpolation
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Synthesis of circular compositional program proofs via abduction
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Inductive invariant generation via abductive inference
Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
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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 linear inequalities over integers.