A 3-CNF-SAT descriptor algebra and the solution of the P=NP conjecture

TL;DR

This paper introduces a novel descriptor algebra approach to decide 3-CNF-SAT satisfiability, providing a bounded exponential complexity algorithm that could impact the P vs NP problem.

Contribution

It proposes a new descriptor-based method for 3-CNF-SAT, offering a bounded exponential complexity solution that advances understanding of satisfiability problems.

Findings

Decides 3-CNF-SAT with bounded exponential complexity

Provides an algorithm with complexity O(2^490)

Uses descriptor functions to avoid solution exploration

Abstract

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we investigate a descriptor approach based on lattice properties. This paper proposes a new way to decide the satisfiability of any 3-CNF-SAT problem. The analysis of this exact [non heuristical] algorithm shows a strictly bounded exponential complexity. The complexity of any 3-CNF-SAT solution is bounded by O(2^490). This over-estimated bound is reached by an algorithm working on the smallest description (via descriptor functions) of the evolving set of solutions in function of the already considered clauses, without exploring these solutions. Any remark about this paper is warmly welcome.