Resolution and Pebbling Games
We define a collection of Prover-Delayer games to characterise some subsystems of propositional resolution. We give some natural criteria for the games which guarantee lower bounds on the resolution width. By an adaptation of the size-width tradeoff for resolution of  this result also gives lower bounds on proof size.
We also use games to give upper bounds on proof size, and in particular describe a good strategy for the Prover in a certain game which yields a short refutation of the Linear Ordering principle.
Using previous ideas we devise a new algorithm to automatically generate resolution refutations. On bounded width formulas, our algorithm is as least as good as the width based algorithm of . Moreover, it finds short proofs of the Linear Ordering principle when the variables respect a given order.
Finally we approach the question of proving that a formula F is hard to refute if and only if is “almost” satisfiable. We prove results in both directions when “almost satisfiable” means that it is hard to distuinguish F from a satisfiable formula using limited pebbling games.
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- 2.Alekhnovich, M., Razborov, A.A.: Resolution is not automatizable unless W[P] is not tractable. In: 42nd IEEE Symposium on Foundations of Computer Science, FOCS 2001, pp. 210–219 (2001)Google Scholar
- 3.Atserias, A., Dalmau, V.: A combinatorial characterization of Resolution Width. In: 18th IEEE Conference on Computational Complexity (CCC), pp. 239–247 (2003)Google Scholar
- 6.Beame, P., Kautz, H.: A Sabharwal Understanding the power of clause learning. In: Proceedings IJCAI, pp. 1194–1201 (2003)Google Scholar
- 7.Beame, P., Pitassi, T.: Simplified and Improved Resolution Lower Bounds. In: 37th IEEE Symposium on Foundations of Computer Science, FOCS 1996, pp. 274–282 (1996)Google Scholar
- 8.Ben-Sasson, E., Galesi, N.: Space Complexity of Random Formulae in Resolution. In: 16th IEEE Annual Conference on Computational Complexity, CCC 2001, pp. 42–51 (2001)Google Scholar
- 9.Ben-Sasson, E., Impagliazzo, R., Wigderson, A.: Near optimal separation of treelike and general Resolution. In: Electronic Colloquium on Computational Complexity (ECCC) TR00-005 (2000) To appear in CombinatoricaGoogle Scholar
- 14.Galesi, N., Thapen, N.: The Complexity of Treelike Systems over λ Local Formuale. In: Proceedings of IEEE Conference on Computational Complexity (2004)Google Scholar
- 15.Galesi, N., Thapen, N.: Resolution and Pebbling Games. ECCC Technical Report TR04-112, http://www.eccc.uni-trier.de/eccc-reports/2004/TR04-112/index.html
- 19.Pudlak, P.: Proofs as Games. American Math. Monthly 107(6), 541–550 (2000)Google Scholar
- 20.Pudlák, P., Impagliazzo, R.: A lower bound for DLL algorithms for k-SAT. In: Conference Proceeding of Symposium on Distributed Algorithms, pp. 128–136 (2000)Google Scholar