Print Email Facebook Twitter Newton Series, Coinductively Title Newton Series, Coinductively Author Basold, H. Hansen, H.H. Pin, J.E. Rutten, J. Faculty Technology, Policy and Management Department Engineering, Systems and Services Date 2015-10-29 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. To reference this document use: http://resolver.tudelft.nl/uuid:7a5c1503-5328-4886-bfe8-ac99bf2fda55 Publisher Springer ISBN 978-3-319-25149-3 Source Theoretical Aspects of Computing – ICTAC 2015. Proceedings of the 12th International Colloquium Cali, Colombia, October 29–31, 2015; Lecture Notes in Computer Science 9399; Authors version Other version https://doi.org/10.1007/978-3-319-25150-9_7 Part of collection Institutional Repository Document type conference paper Rights (c) 2015 Springer Files PDF 321616.pdf 341.77 KB Close viewer /islandora/object/uuid:7a5c1503-5328-4886-bfe8-ac99bf2fda55/datastream/OBJ/view