A Polynomial Time Algorithm for 3SAT

TL;DR

This paper claims to present a polynomial time algorithm for 3SAT, implying P=NP by showing 3SAT can be decided efficiently through clause implication techniques.

Contribution

The paper introduces a novel polynomial time algorithm for 3SAT based on clause implication and contradiction derivation methods.

Findings

The algorithm can derive contradictions in polynomial time for unsatisfiable instances.

It reduces the problem to processing clauses of length 3 or less, avoiding exponential complexity.

The results suggest P=NP, challenging the current understanding of computational complexity.

Abstract

It is shown that any two clauses in an instance of 3SAT sharing the same terminal which is positive in one clause and negated in the other can imply a new clause composed of the remaining terms from both clauses. Clauses can also imply other clauses as long as all the terms in the implying clauses exist in the implied clause. It is shown an instance of 3SAT is unsatisfiable if and only if it can derive contradicting 1-terminal clauses in exponential time. It is further shown that these contradicting clauses can be implied with the aforementioned techniques without processing clauses of length 4 or greater, reducing the computation to polynomial time. Therefore there is a polynomial time algorithm that will produce contradicting 1-terminal clauses if and only if the instance of 3SAT is unsatisfiable. Since such an algorithm exists and 3SAT is NP-Complete, P = NP.