The monotone circuit complexity of Boolean functions
Combinatorica
Many hard examples for resolution
Journal of the ACM (JACM)
Resolution proofs of generalized pigeonhole principles. (Note)
Theoretical Computer Science
Exponential lower bounds for the pigeonhole principle
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first 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
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
An Optimal Lower Bound for Resolution with 2-Conjunctions
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
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
Mean-payoff games and propositional proofs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHPn cn and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are known. As a consequence to the result about the weak pigeonhole principle, Res(log) is exponentially more powerful than Res(2). Also we prove that Resolution cannot polynomially simulate Res(2), and that Res(2) does not have feasible monotone interpolation solving an open problem posed by Krajíček.