PPSZ for General k-SAT - Making Hertli's Analysis Simpler and 3-SAT Faster

Authors Dominik Scheder, John P. Steinberger

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Dominik Scheder
John P. Steinberger

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Dominik Scheder and John P. Steinberger. PPSZ for General k-SAT - Making Hertli's Analysis Simpler and 3-SAT Faster. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


The currently fastest known algorithm for k-SAT is PPSZ named after its inventors Paturi, Pudlak, Saks, and Zane. Analyzing its running time is much easier for input formulas with a unique satisfying assignment. In this paper, we achieve three goals. First, we simplify Hertli's analysis for input formulas with multiple satisfying assignments. Second, we show a "translation result": if you improve PPSZ for k-CNF formulas with a unique satisfying assignment, you will immediately get a (weaker) improvement for general k-CNF formulas. Combining this with a result by Hertli from 2014, in which he gives an algorithm for Unique-3-SAT slightly beating PPSZ, we obtain an algorithm beating PPSZ for general 3-SAT, thus obtaining the so far best known worst-case bounds for 3-SAT.
  • Boolean satisfiability
  • exponential algorithms
  • randomized algorithms


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