Recognizable Series on Hypergraphs

TL;DR

This paper introduces Hypergraph Weighted Models (HWM), a tensor network framework for hypergraph series recognition, generalizing rational series on strings and trees, with analysis of properties and conditions for recognizability.

Contribution

It presents a new tensor network-based model for hypergraph series recognition, extending classical series concepts to hypergraphs and analyzing its properties.

Findings

HWM generalizes rational series to hypergraphs.

Conditions for finite support series recognizability are identified.

Properties of the HWM model are established.

Abstract

We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family is said to be recognizable if there exists a HWM that computes it. This model generalizes the notion of rational series on strings and trees. We prove some properties of the model and study at which conditions finite support series are recognizable.