A Satisfiability algorithm based on Simple Spinors of the Clifford algebra of $\mathbb{R}^{n,n}$

TL;DR

The paper introduces a novel polynomial-time unsatisfiability test for Boolean problems using Clifford algebra, moving away from traditional combinatorial methods.

Contribution

It refines the Clifford algebra formulation of SAT and presents a continuous, algebraic approach to unsatisfiability testing that is not combinatorial.

Findings

Proposes a polynomial-time unsatisfiability algorithm

Refines Clifford algebra formulation of SAT

Moves beyond combinatorial methods

Abstract

We refine the formulation of the Boolean satisfiability problem with $n$ Boolean variables in Clifford algebra ${\cal C}\ell(\mathbb{R}^{n,n})$ [3] and exploit this continuous setting to outline a new unsatisfiability test. This algorithm is not combinatorial and can prove unsatisfiability in polynomial time.