Variable Dependencies and Q-Resolution
We propose Q(D)-resolution, a proof system for Quantified Boolean Formulas. Q(D)-resolution is a generalization of Q-resolution parameterized by a dependency scheme D. This system is motivated by the generalization of the QDPLL algorithm using dependency schemes implemented in the solver DepQBF. We prove soundness of Q(D)-resolution for a dependency scheme D that is strictly more general than the standard dependency scheme; the latter is currently used by DepQBF. This result is obtained by proving correctness of an algorithm that transforms Q(D)-resolution refutations into Q-resolution refutations and could be of independent practical interest. We also give an alternative characterization of resolution- path dependencies in terms of directed walks in a formula’s implication graph which admits an algorithmically more advantageous treatment.
Unable to display preview. Download preview PDF.
- 4.Bubeck, U.: Model-based transformations for quantified Boolean formulas. Ph.D. thesis. University of Paderborn (2010)Google Scholar
- 7.Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An algorithm to evaluate Quantified Boolean Formulae and its experimental evaluation. Journal of Automated Reasoning 28(2) (2002)Google Scholar
- 9.Goultiaeva, A., Gelder, A.V., Bacchus, F.: A uniform approach for generating proofs and strategies for both true and false QBF formulas. In: Walsh, T. (ed.) Proceedings of IJCAI 2011, pp. 546–553. IJCAI/AAAI (2011)Google Scholar
- 12.Lonsing, F.: Dependency Schemes and Search-Based QBF Solving: Theory and Practice. Ph.D. thesis. Johannes Kepler University, Linz, Austria (April 2012)Google Scholar
- 17.Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. Theory of Computing, pp. 1–9. ACM (1973)Google Scholar