Many hard examples for resolution
Journal of the ACM (JACM)
Exponential lower bounds for the pigeonhole principle
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The Complexity of the Hajos Calculus
SIAM Journal on Discrete Mathematics
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Using caching to solve larger probabilistic planning problems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
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
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
A Switching Lemma for Small Restrictions and Lower Bounds for k - DNF Resolution
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
SATO: An Efficient Propositional Prover
CADE-14 Proceedings of the 14th 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
Algorithms and Complexity Results for #SAT and Bayesian Inference
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
Toward a Model for Backtracking and Dynamic Programming
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Value elimination: bayesian inference via backtracking search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
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We consider extensions of the DPLL approach to satisfiability testing that add a version of memoization, in which formulas that the algorithm has previously shown to be unsatisfiable are remembered for later use. Such formula caching algorithms have been suggested for satisfiability and stochastic satisfiability by several authors. We formalize these methods by developing extensions of the fruitful connection that has previously been developed between DPLL algorithms for satisfiability and tree-like resolution proofs of unsatisfiability. We analyze a number of variants of these formula caching methods and characterize their strength in terms of proof systems. These proof systems are new and simple, and have a rich structure. We compare them to several studied proof systems: tree-like resolution, regular resolution, general resolution, Res(k), and Frege systems and present both simulation and separations. One of our most interesting results is the introduction of a natural and implementable form of DPLL with caching, FCWreason. This system is surprisingly powerful: we prove that it can polynomially simulate regular resolution, and furthermore, it can produce short proofs of some formulas that require exponential-size resolution proofs.