Recognizable series on hypergraphs
arXiv preprint arXiv:1404.7533, 2014•arxiv.org
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.
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.
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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