Chain, Generalization of Covering Code, and Deterministic Algorithm for k-SAT

TL;DR

This paper introduces a new deterministic algorithm for k-SAT that improves the upper bounds on solving time, utilizing chains, generalized covering codes, and enhanced branching strategies.

Contribution

It presents the fastest known deterministic algorithm for k-SAT, combining novel techniques like chains and generalized covering codes, and improves bounds for 3-SAT.

Findings

Improved upper bound for k-SAT: (2-2/k)^{n + o(n)}

Enhanced branching algorithm for 3-SAT with bound 1.32793^n

Introduction of chains and generalized covering codes for algorithm analysis

Abstract

We present the current fastest deterministic algorithm for $k$-SAT, improving the upper bound $(2-2/k)^{n + o(n)}$ dues to Moser and Scheder [STOC'11]. The algorithm combines a branching algorithm with the derandomized local search, whose analysis relies on a special sequence of clauses called chain, and a generalization of covering code based on linear programming. We also provide a more ingenious branching algorithm for $3$-SAT to establish the upper bound $1.32793^n$, improved from $1.3303^n$.