Journal of the ACM (JACM)
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Some consequences of cryptographical conjectures for S12 and EF
Information and Computation - Special issue: logic and computational complexity
Space complexity in propositional calculus
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A new proof of the weak pigeonhole principle
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Information and Computation
Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
Lower Bounds for the Weak Pigeonhole Principle Beyond Resolution
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
On the Structure of the Simulation Order of Proof Systems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On the automatizability of resolution and related propositional proof systems
Information and Computation
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
The Depth of Resolution Proofs
Studia Logica
Relativisation provides natural separations for resolution-based proof systems
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
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We analyze size and space complexity of Res(k), a family of proof systems introduced by Kraj铆驴ek in [16] which extend Resolution by allowing disjunctions of conjunctions of up to k 驴 1 literals. We prove the following results: (1) The treelike Res(k) proof systems form a strict hierarchy with respect to proof size and also with respect to space. (2) Resolution polynomially simulates treelike Res(k), and is almost exponentially separated from treelike Res(k). (3) The space lower bounds known for Resolution also carry over to Res(k). We obtain almost optimal space lower bounds for PHPn, GTn, Random Formulas, CTn, and Tseitin Tautologies.