Introduction to algorithms
Witnesses for Boolean matrix multiplication and for transitive closure
Journal of Complexity
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Counter-Example Based Predicate Discovery in Predicate Abstraction
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
The LPSAT Engine & Its Application to Resource Planning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Lazy Theorem Proving for Bounded Model Checking over Infinite Domains
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Abstract Congruence Closure and Specializations
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Combining Proof-Producing Decision Procedures
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Knuth--Bendix completion of theories of commuting group endomorphisms
Information Processing Letters
Modular SMT proofs for fast reflexive checking inside coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Green: reducing, reusing and recycling constraints in program analysis
Proceedings of the ACM SIGSOFT 20th International Symposium on the Foundations of Software Engineering
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We consider the problem of finding irredundant bases for inconsistent sets of equalities and disequalities. These are subsets of inconsistent sets which do not contain any literals which do not contribute to the unsatisfiability in an essential way, and can therefore be discarded. The approach we are pursuing here is to decorate derivations with proofs and to extract irredundant sets of assumptions from these proofs. This requires specialized operators on proofs, but the basic inference systems are otherwise left unchanged. In particular, we include justifying inference systems for union-find structures and abstract congruence closure, but our constructions can also be applied to other inference systems such as Gaussian elimination.