Recognizable Series on Hypergraphs
نویسندگان
چکیده
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.
منابع مشابه
Recognizable Sets of Graphs, Hypergraphs and Relational Structures: A Survey
New results on the recognizability of sets of finite graphs, hypergraphs and relational structures are presented. The general framework of this research which associates tightly algebraic notions (equational and recognizable sets) and Monadic Second-Order logic (for defining sets and transformations of graphs, hypergraphs and relational structures) is reviewed. The lecture [3] is based on two s...
متن کاملRecognizability, hypergraph operations, and logical types
We study several algebras of graphs and hypergraphs and the corresponding notions of equational sets and recognizable sets. We generalize and unify several existing results which compare the associated equational and recognizable sets. The basic algebra on relational structures is based on disjoint union and quantifier-free definable operations. We expand it to an equivalent one by adding opera...
متن کاملAnomaly Detection using Scan Statistics on Time Series Hypergraphs
We present a theory of scan statistics on hypergraphs and apply the methodology to a time series of email data. This approach is of interest because a hypergraph is better suited to email data than a graph. This is due to the fact that a hypergraph can contain all the recipients of a message in a single hyperedge rather than treating each recipient separately in a graph. The result shows that s...
متن کاملOn the supports of recognizable series over a field and a single letter alphabet
We prove that the support of a recognizable series over a field of characteristic zero and a single letter alphabet is recognizable. This provides an answer to a question of Kirsten [4]. Then we give an example of a recognizable series over a field of prime characteristic and a single letter alphabet whose support is not recognizable which provides an answer to a question of Kirsten and Quaas [5].
متن کاملDoes o-Substitution Preserve Recognizability?
Substitution operations on tree series are at the basis of systems of equations (over tree series) and tree series transducers. Tree series transducers seem to be an interesting transformation device in syntactic pattern matching. In this contribution, it is shown that o-substitution preserves recognizable tree series provided that the target tree series is linear and the semiring is idempotent...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015