# The Boolean SATisfiability Problem in Clifford algebra

## TL;DR

This paper introduces a novel formulation of the Boolean Satisfiability Problem using Clifford algebra, providing a new necessary and sufficient condition for unsatisfiability and outlining an algorithm with potential theoretical benefits.

## Contribution

It presents a unique spinor-based formulation of SAT and proposes an algorithm for testing unsatisfiability with promising theoretical characteristics.

## Key findings

- Provides a necessary and sufficient condition for SAT unsatisfiability
- Introduces a spinor-based formulation of Boolean logic
- Outlines an algorithm with potential theoretical advantages

## Abstract

We present a formulation of the Boolean Satisfiability Problem in spinor language that allows to give a necessary and sufficient condition for unsatisfiability. With this result we outline an algorithm to test for unsatisfiability with possibly interesting theoretical properties.