Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines

TL;DR

This paper introduces a new complete problem for a real nondeterministic polynomial-time complexity class, focusing on cross product expressions, expanding the understanding of computational complexity over the reals.

Contribution

It presents a novel complete problem involving cross product terms for the Blum-Shub-Smale machine complexity class over the reals.

Findings

Identifies a new complete problem for the class

Connects geometric algebra with computational complexity

Expands the set of known complete problems for real algebraic geometry

Abstract

Nondeterministic polynomial-time Blum-Shub-Smale Machines over the reals give rise to a discrete complexity class between NP and PSPACE. Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete (under many-one reduction by polynomial-time Turing machines) for this class. We exhibit a new one based on questions about expressions built from cross products only.