Super strong ETH is true for PPSZ with small resolution width
Scheder, D. and Talebanfard, N.
(2020)
Super strong ETH is true for PPSZ with small resolution width.
In: Saraf, S., (ed.)
35th Computational Complexity Conference (CCC 2020).
35th Computational Complexity Conference (CCC 2020), 28-31 Jul 2020, Saarbrücken, Germany (Virtual).
Leibniz International Proceedings in Informatics (LIPIcs), 169
.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
, 3:1-3:12.
ISBN 9783959771566
Abstract
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).
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