2026-07-20T05:38:58Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:3440 2024-03-06T10:34:09Z ddc:004 open_access

An Approximation Algorithm for #k-SAT Thurley, Marc #k-SAT approximate counting exponential algorithms We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k>=3 within a running time that is not only non-trivial, but also significantly better than that of the currently fastest exact algorithms for the problem. More precisely, our algorithm is a randomized approximation scheme whose running time depends polynomially on the error tolerance and is mildly exponential in the number n of variables of the input formula. For example, even stipulating sub-exponentially small error tolerance, the number of solutions to 3-CNF input formulas can be approximated in time O(1.5366^n). For 4-CNF input the bound increases to O(1.6155^n). We further show how to obtain upper and lower bounds on the number of solutions to a CNF formula in a controllable way. Relaxing the requirements on the quality of the approximation, on k-CNF input we obtain significantly reduced running times in comparison to the above bounds. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc Thurley 2012 Is Part Of LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2012.78 urn:nbn:de:0030-drops-34400 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.78 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode