On the complexity of cutting-plane proofs
Discrete Applied Mathematics
Lower bounds for cutting planes proofs with small coefficients
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Lower bounds for the polynomial calculus and the Gröbner basis algorithm
Computational Complexity
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Ramsey's Theorem in Bounded Arithmetic
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
The Cutting Plane Proof System with Bounded Degree of Falsity
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Examples of hard tautologies in the propositional calculus
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Optimality of size-degree tradeoffs for polynomial calculus
ACM Transactions on Computational Logic (TOCL)
A note on propositional proof complexity of some Ramsey-type statements
Archive for Mathematical Logic
The Ramsey number R(3, t) has order of magnitude t2/log t
Random Structures & Algorithms
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Simulating cutting plane proofs with restricted degree of falsity by resolution
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Boolean Function Complexity: Advances and Frontiers
Boolean Function Complexity: Advances and Frontiers
A lower bound on the size of resolution proofs of the Ramsey theorem
Information Processing Letters
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Ramsey's Theorem is a cornerstone of combinatorics and logic. In its simplest formulation it says that there is a function r such that any simple graph with r(k,s) vertices contains either a clique of size k or an independent set of size s. We study the complexity of proving upper bounds for the number r(k,k). In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k,k)≤4k" requires cutting planes proof of high rank. In order to do that we show a protection lemma which could be of independent interest.