The monotone circuit complexity of Boolean functions
Combinatorica
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
Lower bounds for cutting planes proofs with small coefficients
STOC '95 Proceedings of the twenty-seventh 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
An exponential lower bound for the size of monotone real circuits
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A new proof of the weak pigeonhole principle
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
On Reducibility and Symmetry of Disjoint NP-Pairs
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Lower Bounds for the Weak Pigeonhole Principle Beyond Resolution
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Non-Automatizability of Bounded-Depth Frege Proofs
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
Optimality of size-width tradeoffs for resolution
Computational Complexity
Tree Resolution Proofs of the Weak Pigeon-Hole Principle
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 complexity of resolution with bounded conjunctions
Theoretical Computer Science
Classes of representable disjoint NP-pairs
Theoretical Computer Science
Artificial Intelligence
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Relativisation provides natural separations for resolution-based proof systems
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Disjoint NP-pairs from propositional proof systems
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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We analyse the possibility that a system that simulates Resolution is automatizable. We call this notion "weak automatizability". We prove that Resolution is weakly automatizable if and only if Res(2) has feasible interpolation. In order to prove this theorem, we show that Res(2) has polynomial-size proofs of the reflection principle of Resolution (and of any Res(k)), which is a version of consistency. We also show that Resolution proofs of its own reflection principle require slightly subexponential size. This gives a better lower bound for the monotone interpolation of Res(2) and a better separation from Resolution as a byproduct. Finally, the techniques for proving these results give us a new complexity measure for Resolution that refines the width of Ben-Sasson and Wigderson. The new measure and techniques suggest a new algorithm to find Resolution refutations, and a way to obtain a large class of examples that have small Resolution refutations but require relatively large width. This answers a question of Alekhnovich and Razborov related to whether Resolution is automatizable in quasipolynomial-time.