A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
The complexity of resolution procedures for theorem proving in the propositional calculus.
The complexity of resolution procedures for theorem proving in the propositional calculus.
On the lengths of proofs in the propositional calculus.
On the lengths of proofs in the propositional calculus.
Examples of hard tautologies and worst-case complexity results for propositional proof systems
Examples of hard tautologies and worst-case complexity results for propositional proof systems
Graph Theory With Applications
Graph Theory With Applications
Annals of Mathematics and Artificial Intelligence
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
A note on propositional proof complexity of some Ramsey-type statements
Archive for Mathematical Logic
A lower bound on the size of resolution proofs of the Ramsey theorem
Information Processing Letters
A rank lower bound for cutting planes proofs of ramsey's theorem
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
The complexity of proving that a graph is ramsey
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We present examples of hard tautologies in propositional calculus by encoding instances of the assertions made by Ramsey's theorem. We provide evidence that these tautologies are indeed hard by 1. showing that there are no short proofs for these tautologies in certain restricted classes of proof systems; 2. relating a proof of these tautologies to the problem of determining the diagonal Ramsey numbers for graphs.