A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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
A PSPACE Complete Problem Related to a Pebble Game
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
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
Storage requirements for deterministic polynomialtime recognizable languages
Journal of Computer and System Sciences
The PSPACE-Completeness of Black-White Pebbling
SIAM Journal on Computing
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
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The Prover/Delayer game is a combinatorial game that can be used to prove upper and lower bounds on the size of Tree Resolution proofs, and also perfectly characterizes the space needed to compute them. As a proof system, Tree Resolution forms the underpinnings of all DPLL-based SAT solvers, so it is of interest not only to proof complexity researchers, but also to those in the area of propositional reasoning. In this paper, we prove the PSPACE-Completeness of the Prover/Delayer game as well as the problem of predicting Tree Resolution space requirements, where space is the number of clauses that must be kept in memory simultaneously during the computation of a refutation. Since in practice memory is often a limiting resource, researchers developing SAT solvers may wish to know ahead of time how much memory will be required for solving a certain formula, but the present result shows that predicting this is at least as hard as it would be to simply find a refutation.