Recognizable Series on Hypergraphs

Recognizable Series on Hypergraphs

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 compute...

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Veröffentlicht in:arXiv.org 2014-10
Hauptverfasser: Bailly, Raphaël, Denis, François, Rabusseau, Guillaume
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Graph theory
Graphs
Mathematical analysis
Series (mathematics)
Strings
Tensors
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Denis, François
Rabusseau, Guillaume
description 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.
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subjects Graph theory
Graphs
Mathematical analysis
Series (mathematics)
Strings
Tensors
title Recognizable Series on Hypergraphs
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