Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
A tight bound for black and white pebbles on the pyramid
Journal of the ACM (JACM)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Information and Computation
Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Space Complexity in Propositional Calculus
SIAM Journal on Computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Variations of a pebble game on graphs
Variations of a pebble game on graphs
Space complexity of random formulae in resolution
Random Structures & Algorithms
A combinatorial characterization of treelike resolution space
Information Processing Letters
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Exponential Time/Space Speedups for Resolution and the PSPACE-completeness of Black-White Pebbling
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A simplified way of proving trade-off results for resolution
Information Processing Letters
The complexity of the Hajós calculus for planar graphs
Theoretical Computer Science
On minimal unsatisfiability and time-space trade-offs for k-DNF resolution
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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)
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
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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
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Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field of proof complexity, the resources of time and memory correspond to the length and space of resolution proofs. There has been a long line of research trying to understand these proof complexity measures, as well as relating them to the width of proofs, i.e., the size of the largest clause in the proof, which has been shown to be intimately connected with both length and space. While strong results have been proven for length and width, our understanding of space is still quite poor. For instance, it has remained open whether the fact that a formula is provable in short length implies that it is also provable in small space (which is the case for length versus width), or whether on the contrary these measures are completely unrelated in the sense that short proofs can be arbitrarily complex with respect to space. In this paper, we present some evidence that the true answer should be that the latter case holds and provide a possible roadmap for how such an optimal separation result could be obtained. We do this by proving a tight bound of Theta(√(n)) on the space needed for so-called pebbling contradictions over pyramid graphs of size n. Also, continuing the line of research initiated by (Ben-Sasson 2002) into trade-offs between different proof complexity measures, we present a simplified proof of the recent length-space trade-off result in (Hertel and Pitassi 2007), and show how our ideas can be used to prove a couple of other exponential trade-offs in resolution.