Short proofs for tricky formulas
Acta Informatica
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
An exponential separation between regular and general resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Implementing the Davis–Putnam Method
Journal of Automated Reasoning
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
The Search Efficiency of Theorem Proving Strategies
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
A Study of Proof Search Algorithms for Resolution and Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Optimality of size-width tradeoffs for resolution
Computational Complexity
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
An Exponential Lower Bound for Width-Restricted Clause Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Clause learning can effectively P-simulate general propositional resolution
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Verifying propositional unsatisfiability: pitfalls to avoid
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
On the power of clause-learning SAT solvers with restarts
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
An improved separation of regular resolution from pool resolution and clause learning
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Pool Resolution for propositional CNF formulas is introduced. Its relationship to state-of-the-art satisfiability solvers is explained. Every regular-resolution derivation is also a pool-resolution derivation. It is shown that a certain family of formulas, called NT**(n) has polynomial sized pool-resolution refutations, whereas the shortest regular refutations have an exponential lower bound. This family is a variant of the GT(n) family analyzed by Bonet and Galesi (FOCS 1999), and the GT’n family shown to require exponential-length regular-resolution refutations by Alekhnovitch, Johannsen, Pitassi and Urquhart (STOC 2002). Thus, Pool Resolution is exponentially stronger than Regular Resolution. Roughly speaking a general-resolution derivation is a pool-resolution derivation if its directed acyclic graph (DAG) has a depth-first search tree that satisfies the regularity restriction: on any path in this tree no resolution variable is repeated. In other words, once a clause is derived at a node and used by its tree parent, its derivation is forgotten, and subsequent uses of that clause treat it as though it were an input clause. This policy is closely related to DPLL search with recording of so-called conflict clauses. Variations of DPLL plus conflict analysis currently dominate the field of high-performance satisfiability solving. The power of Pool Resolution might provide some theoretical explanation for their success.