Multilinear representations of Free PROs

TL;DR

This paper introduces a multilinear framework for representing PROs using hypermatrices, linking algebraic structures with automata theory, and providing new tools for understanding free PROs.

Contribution

It develops a novel multilinear representation approach for PROs, especially free PROs, using hypermatrices, and explores their connection to automata theory.

Findings

Established a PRO structure on hypermatrices.

Defined multilinear representations of PROs, including free PROs.

Connected PRO representations with automata theory.

Abstract

We describe a structure of PRO on hypermatrices. This structure allows us to define multilinear representations of PROs and in particular of free Pros. As an example of applications, we investigate the relations of the representations of Pros with the theory of automata.