Algorithmic problems in right-angled Artin groups: complexity and applications

TL;DR

This paper investigates the computational complexity of various algorithmic problems in right-angled Artin groups, many related to graph theory, with a focus on their implications for cryptography.

Contribution

It introduces new algorithmic problems in right-angled Artin groups and analyzes their complexity, highlighting applications to cryptography.

Findings

Several problems are shown to be computationally hard

New algorithms are proposed for specific problems

Applications to cryptographic protocols are discussed

Abstract

In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with a view towards applications to cryptography.