Super Strong ETH Is True for PPSZ with Small Resolution Width

Authors Dominik Scheder, Navid Talebanfard

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Author Details

Dominik Scheder
  • Shanghai Jiaotong University, China
Navid Talebanfard
  • Institute of Mathematics, The Czech Academy of Sciences, Prague, Czech Republic

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Dominik Scheder and Navid Talebanfard. Super Strong ETH Is True for PPSZ with Small Resolution Width. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We construct k-CNFs with m variables on which the strong version of PPSZ k-SAT algorithm, which uses resolution of width bounded by O(√{log log m}), has success probability at most 2^{-(1-(1 + ε)2/k)m} for every ε > 0. Previously such a bound was known only for the weak PPSZ algorithm which exhaustively searches through small subformulas of the CNF to see if any of them forces the value of a given variable, and for strong PPSZ the best known previous upper bound was 2^{-(1-O(log(k)/k))m} (Pudlák et al., ICALP 2017).

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
  • k-SAT
  • PPSZ
  • Resolution


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