Abstract
#kSAT is a complex problem equivalent to calculate the cardinalities of the null sets of conjunctive forms consisting of clauses with an uniform length. Each such null set is the union of linear varieties of uniform dimension in the hypercube. Here we study the class of sets in the hypercube that can be realized as such null sets. We look toward to characterize their cardinalities and the number of ways that they can be expressed as unions of linear varieties of uniform dimension. Using combinatorial and graph theory argumentations, we give such characterizations for very extremal values of k, either when it is very small or close to the hypercube dimension, and of the number of clauses appearing in an instance, either of value 2, or big enough to get a contradiction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Birnbaum, E., Lozinskii, E.L.: The good old Davis-Putnam procedure helps counting models. Journal of Artificial Intelligence 10, 457–477 (1999)
Linial, N., Nisan, N.: Approximate inclusion-exclusion. Combinatorica 10, 349–365 (1990)
Iwama, K., Matsuura, A.: Inclusion-exclusion for k-CNF formulas. In: Proc. of 5th International Symposium on the Theory and Applications of Satisfiability Testing, SAT2002 (2002)
Bacchus, F., Dalmao, S., Pitassi, T.: DPLL with caching: A new algorithm for #SAT and Bayesian inference. In: Proc. 44th Annual Symposium on Foundations of Computer Science. IEEE, Los Alamitos (2003)
Zuckerman, D.: On unapproximable versions of NP-complete problems. SIAM J. Computing 25, 1293–1304 (1996)
Bürgisser, P.: Cook’s versus Valiant’s hypothesis. Theoret. Comp. Sci. 235, 71–88 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Morales-Luna, G. (2005). Geometric Aspects Related to Solutions of #kSAT. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_14
Download citation
DOI: https://doi.org/10.1007/11579427_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29896-0
Online ISBN: 978-3-540-31653-4
eBook Packages: Computer ScienceComputer Science (R0)