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)
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth 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
Space complexity in propositional calculus
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Resolution Proofs, Exponential Bounds, and Kolmogorov Complexity
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
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
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A combinatorial characterization of treelike resolution space
Information Processing Letters
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Towards an optimal separation of space and length in resolution
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
What Is a Real-World SAT Instance?
Proceedings of the 2007 conference on Artificial Intelligence Research and Development
A simplified way of proving trade-off results for resolution
Information Processing Letters
Refutation by randomised general resolution
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The PSPACE-Completeness of Black-White Pebbling
SIAM Journal on Computing
The Depth of Resolution Proofs
Studia Logica
Autonomous resolution based on DNA strand displacement
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
Local search for unsatisfiability
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Game characterizations and the PSPACE-completeness of tree resolution space
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Relating proof complexity measures and practical hardness of SAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Some trade-off results for polynomial calculus: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
Towards an understanding of polynomial calculus: new separations and lower bounds
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Implicit learning of common sense for reasoning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We introduce a new way to measure the space needed in resolution refutations of CNF formulas in propositional logic. With the former definition (1994, B. H. Kleine and T. Lettman, "Aussangenlogik: Deduktion und Algorithmen, Teubner, Stuttgart) 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 us 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 relationships to the size of the refutation. We also give upper and lower bounds on the space needed for the resolution of unsatisfiable formulas. We show that Tseitin formulas associated to a certain kind of expander graphs of n nodes need resolution space n-c for some constant c. Measured on the number of clauses, this result is the best possible. We also show that the formulas expressing the general pigeonhole principle with n holes and more than n pigeons need space n+1 independent of the number of pigeons. Since a matching space upper bound of n+1 for these formulas exists, the obtained bound is exact. We also point to a possible connection between resolution space and resolution width, another measure for the complexity of resolution refutations. 2001 Elsevier Science.