Journal of the ACM (JACM)
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Information and Computation
Space Complexity in Propositional Calculus
SIAM Journal on Computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Space Complexity of Random Formulae in Resolution
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Resolution is Not Automatizable Unless W[P] is Tractable
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The Complexity of Treelike Systems over "-Local Formulae
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Resolution Width and Cutting Plane Rank Are Incomparable
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
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We define a collection of Prover-Delayer games to characterise some subsystems of propositional resolution. We give some natural criteria for the games which guarantee lower bounds on the resolution width. By an adaptation of the size-width tradeoff for resolution of [10] this result also gives lower bounds on proof size. We also use games to give upper bounds on proof size, and in particular describe a good strategy for the Prover in a certain game which yields a short refutation of the Linear Ordering principle. Using previous ideas we devise a new algorithm to automatically generate resolution refutations. On bounded width formulas, our algorithm is as least as good as the width based algorithm of [10]. Moreover, it finds short proofs of the Linear Ordering principle when the variables respect a given order. Finally we approach the question of proving that a formula F is hard to refute if and only if is “almost” satisfiable. We prove results in both directions when “almost satisfiable” means that it is hard to distuinguish F from a satisfiable formula using limited pebbling games.