GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Computer Algorithms: Introduction to Design and Analysis
Computer Algorithms: Introduction to Design and Analysis
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Verification of Proofs of Unsatisfiability for CNF Formulas
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Verifying propositional unsatisfiability: pitfalls to avoid
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Extended resolution proofs for conjoining BDDs
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Generalized conflict-clause strengthening for satisfiability solvers
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Two techniques for minimizing resolution proofs
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Contributions to the theory of practical quantified boolean formula solving
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
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Recent empirical results show that recursive, or expensive, conflict-clause minimization is quite beneficial on industrial-style propositional satisfiability problems. The details of this procedure appear to be unpublished to date, but may be found in the open-source code of MiniSat 2.0, for example. Biere reports that proof traces are made more complicated when conflict-clause minimization is used because some clauses need to be resolved upon multiple times during the minimization procedure as found in MiniSat 2.0. Biere proposes a proof-trace format in which the set of clause numbers needed for a certain derivation is given, but their order is not specified. This paper presents a new procedure for conflict-clause minimization that is slightly more efficient and, more importantly, discovers a correct order so that each clause used for the derivation is resolved upon only once. This permits the proof trace to specify the order in which to use the clauses, greatly reducing the burden on software that processes the proof trace. The method is validated on the unsatisfiable formulas used for industrial benchmarks in the verified-unsatisfiable track of the SAT 2007 competition.