Journal of the ACM (JACM)
Resolution proofs of generalized pigeonhole principles. (Note)
Theoretical Computer Science
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Lower bounds for the polynomial calculus
Computational Complexity
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Propositional proof complexity: past, present, and future
Current trends in theoretical computer science
Regular resolution lower bounds for the weak pigeonhole principle
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Resolution lower bounds for the weak pigeonhole principle
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Lower Bounds for Propositional Proofs and Independence Results in Bounded Arithmetic
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Proof Complexity of Pigeonhole Principles
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Resolution Lower Bounds for Perfect Matching Principles
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
SymChaff: a structure-aware satisfiability solver
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Parameterized Bounded-Depth Frege Is not Optimal
ACM Transactions on Computation Theory (TOCT)
Some trade-off results for polynomial calculus: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We prove that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2nε), (for some global constant ε 0). One corollary is that a certain propositional formulation of the statement NP ⊄ P/poly does not have short Resolution proofs.