Understanding SAT is in P

TL;DR

This paper introduces a novel concept of understanding based on literal contexts in 3-SAT problems and presents a mechanical process that efficiently determines the existence of such understanding, effectively solving 3-SAT.

Contribution

It proposes a new interpretative framework for 3-SAT and a mechanical process that can efficiently find or confirm the absence of understanding, implying P=NP.

Findings

The process correctly identifies understanding in 3-SAT instances.

The process is efficient and can solve 3-SAT problems.

It demonstrates that SAT can be in P.

Abstract

We introduce the idea of an understanding with respect to a set of clauses as a satisfying truth assignment explained by the contexts of the literals in the clauses. Following this idea, we present a mechanical process that obtains, if it exists, an understanding with respect to a 3-SAT problem instance based on the contexts of each literal in the instance, otherwise it determines that none exists. We demonstrate that our process is correct and efficient in solving 3-SAT.