3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General

TL;DR

This paper extends the bounds of the PPSZ algorithm, originally for Unique k-SAT, to general 3-SAT and 4-SAT cases using a modified approach, improving previous exponential time bounds.

Contribution

It demonstrates that PPSZ bounds apply to general 3-SAT and 4-SAT with a modified algorithm, improving known exponential bounds.

Findings

Improved 3-SAT bound to O(1.308^n)

Improved 4-SAT bound to O(1.469^n)

PPSZ bounds hold for general k-SAT for k=3,4

Abstract

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane [1998] is the fastest known algorithm for Unique k-SAT, where the input formula does not have more than one satisfying assignment. For k>=5 the same bounds hold for general k-SAT. We show that this is also the case for k=3,4, using a slightly modified PPSZ algorithm. We do the analysis by defining a cost for satisfiable CNF formulas, which we prove to decrease in each PPSZ step by a certain amount. This improves our previous best bounds with Moser and Scheder [2011] for 3-SAT to O(1.308^n) and for 4-SAT to O(1.469^n).