Theory of linear and integer programming
Theory of linear and integer programming
Introduction to algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A machine program for theorem-proving
Communications of the ACM
Automatic predicate abstraction of C programs
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Deciding Separation Formulas with 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
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
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
DPLL(T) with exhaustive theory propagation and its application to difference logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Combining Decision Procedures by (Model-)Equality Propagation
Electronic Notes in Theoretical Computer Science (ENTCS)
Solving sparse linear constraints
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
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Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satisfiability, the individual decision procedures need to provide additional functionalities, including equality generation. In this paper, we propose a decision procedure for a conjunction of difference constraints over rationals (where the atomic formulas are of the form x=