Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
An exponential separation between regular and general resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Automatizability of Resolution and Related Propositional Proof Systems
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Optimality of size-width tradeoffs for resolution
Computational Complexity
A combinatorial characterization of treelike resolution space
Information Processing Letters
On the automatizability of resolution and related propositional proof systems
Information and Computation
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Complexity results on DPLL and resolution
ACM Transactions on Computational Logic (TOCL)
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Note: The NP-hardness of finding a directed acyclic graph for regular resolution
Theoretical Computer Science
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
ACM Transactions on Computation Theory (TOCT)
Improved lower bounds for tree-like resolution over linear inequalities
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
The Depth of Resolution Proofs
Studia Logica
Decision procedures for SAT, SAT modulo theories and beyond. the barcelogictools
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
The proof-search problem between bounded-width resolution and bounded-degree semi-algebraic proofs
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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An exponential lower bound for the size of tree-like cutting planes refutations of a certain family of conjunctive normal form (CNF) formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the tree-like versions and the dag-like versions of resolution and cutting planes. In both cases only superpolynomial separations were known [A. Urquhart, Bull. Symbolic Logic, 1 (1995), pp. 425--467; J. Johannsen, Inform. Process. Lett., 67 (1998), pp. 37--41; P. Clote and A. Setzer, in Proof Complexity and Feasible Arithmetics, Amer. Math. Soc., Providence, RI, 1998, pp. 93--117]. In order to prove these separations, the lower bounds on the depth of monotone circuits of Raz and McKenzie in [ Combinatorica, 19 (1999), pp. 403--435] are extended to monotone real circuits.An exponential separation is also proved between tree-like resolution and several refinements of resolution: negative resolution and regular resolution. Actually, this last separation also provides a separation between tree-like resolution and ordered resolution, and thus the corresponding superpolynomial separation of [A. Urquhart, Bull. Symbolic Logic, 1 (1995), pp. 425--467] is extended. Finally, an exponential separation between ordered resolution and unrestricted resolution (also negative resolution) is proved. Only a superpolynomial separation between ordered and unrestricted resolution was previously known [A. Goerdt, Ann. Math. Artificial Intelligence, 6 (1992), pp. 169--184].