TY - JOUR

T1 - Newton series, coinductively

T2 - a comparative study of composition

AU - Basold, Henning

AU - Hansen, Helle

AU - Pin, Jean Éric

AU - Rutten, Jan

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://resolver.tudelft.nl/uuid:58298d28-37bd-4b94-bf2d-1bf59a86e23e

UR - http://www.scopus.com/inward/record.url?scp=85020305083&partnerID=8YFLogxK

U2 - 10.1017/S0960129517000159

DO - 10.1017/S0960129517000159

M3 - Article

AN - SCOPUS:85020305083

SP - 1

EP - 29

JO - Mathematical Structures in Computer Science

JF - Mathematical Structures in Computer Science

SN - 0960-1295

ER -