Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
Resolution Proofs, Exponential Bounds, and Kolmogorov Complexity
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Move Rules and Trade-Offs in the Pebble Game
Proceedings of the 4th GI-Conference on Theoretical Computer Science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Space complexity in propositional calculus
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Information and Computation
Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Homogenization and the Polynominal Calculus
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Lower Bounds for Space in Resolution
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Space complexity of random formulae in resolution
Random Structures & Algorithms
Annals of Mathematics and Artificial Intelligence
Homogenization and the polynomial calculus
Computational Complexity
Verifying time, memory and communication bounds in systems of reasoning agents
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We introduce a new way to measure the space needed in a resolution refutation of a CNF formula in propositional logic. With the former definition [6] the space required for the resolution of any unsatisfiable formula in CNF is linear in the number of clauses. The new definition allows a much finer analysis of the space in the refutation, ranging from constant to linear space. Moreover, the new definition allows to relate the space needed in a resolution proof of a formula to other well studied complexity measures. It coincides with the complexity of a pebble game in the resolution graphs of a formula, and as we show, has strong relationships to the size of the refutation. We also give upper and lower bounds on the space needed for the resolution of unsatisfiable formulas.