Newton series, coinductively

a comparative study of composition

Journal article (2017)

Authors

Henning Basold Radboud Universiteit Nijmegen
H.H. Hansen Energy and Industry
Jean Éric Pin Universite Paris Diderot
Jan Rutten Radboud Universiteit Nijmegen
Research Group
Energy and Industry
Copyright: © 2017 Henning Basold, H.H. Hansen, Jean Éric Pin, Jan Rutten
DOI: https://doi.org/10.1017/S0960129517000159
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Published Date

2017

Language

English

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Research Group

Energy and Industry

Abstract

We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that an operator of the classical difference calculus, the Newton transform, generalises from infinite sequences to weighted languages. We show that the Newton transform is an isomorphism of rings that transforms the Hadamard product of two weighted languages into their infiltration product, and we develop various representations for the Newton transform of a language, together with concrete calculation rules for computing them.

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