The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Introduction to Linear Optimization
Introduction to Linear Optimization
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
CVC: A Cooperating Validity Checker
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
A Framework for Cooperating Decision Procedures
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Proof Generation in the Touchstone Theorem Prover
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Checking validities and proofs with cvc and flea
Checking validities and proofs with cvc and flea
Fractional Collections with Cardinality Bounds, and Mixed Linear Arithmetic with Stars
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Automated deduction for verification
ACM Computing Surveys (CSUR)
An Even Closer Integration of Linear Arithmetic into Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
From propositional satisfiability to satisfiability modulo theories
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A progressive simplifier for satisfiability modulo theories
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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Efficient decision procedures for arithmetic play a very important role in formal verification. In practical examples, however, arithmetic constraints are often mixed with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc. Therefore, decision procedures for arithmetic are especially useful in combination with other decision procedures. The framework for such a combination is implemented at Stanford in the tool called Cooperating Validity Checker (CVC) [SBD02]. This work augments CVC with a decision procedure for the theory of mixed integer linear arithmetic based on the Omega-test [Pug91] extended to be online and proof producing. These extensions are the most important and challenging part of the work, and are necessary to make the combination efficient in practice.