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

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.