A combinatorial characterization of treelike resolution space

Authors:
Juan Luis Esteban;Jacobo Torán
Affiliations:
Dept. L.S.I., U. Politècnica de Catalunya, c/Jordi Girona Salgado 1-3, E08034 Barcelona, Spain;Theoretische Informatik, Universität Ulm, Oberer Eselsberg, D-89069 Ulm, Germany
Venue:
Information Processing Letters
Year:
2003

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Abstract

We show that the Player-Adversary game of Pudlák and Impagliazzo [A lower bound for DLL algorithms for k-SAT, in: Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, 2000, pp. 128-136] played over CNF propositional formulas gives an exact characterization of the space needed in treelike resolution refutations. This characterization is purely combinatorial and independent of the notion of resolution. We use this characterization to give for the first time a separation between the space needed in treelike and general resolution.