Abstract
The currently fastest known algorithm for k-SAT is PPSZ, named afterits inventors (Paturi et al. in J ACM 52(3):337-364, 2005. http://dx.doi.org/10.1145/1066100.1066101). Analyzing its running timeis much easier for input formulas with a unique satisfying assignment.In this paper, we achieve three goals. First, we simplify the analysisof Hertli (in 2011 IEEE 52nd Annual Symposium on Foundations ofComputer Science-FOCS 2011, Los Alamitos, 2011) for input formulaswith multiple satisfying assignments. Second, we show a “liftingresult”: if you improve PPSZ for k-CNF formulas with a unique satisfyingassignment, you will immediately get a (weaker) improvement forgeneral k-CNF formulas. In combination this with results by Hansen etal. (in Charikar and Cohen (ed) Proceedings of the 51st Annual ACMSIGACT Symposium on Theory of Computing, 2019) and Scheder (in62nd IEEE Annual Symposium on Foundations of Computer Science,2021), who all prove improved time bounds for Unique-k-SAT, this givesimproved bounds for general k-SAT. We also generalize our results tothe domain of Constraint Satisfaction Problems, i.e., satisfiability withmore than two truth values.
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