We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shue, (iii) the in ltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a nal coalgebra, we use coinduction to prove that a classical operator from di erence calculus in mathematics: the Newton transform, generalises (from in nite sequences) to weighted lan- guages. We show that the Newton transform is an isomorphism of rings that transforms the Hadamard product of two weighted languages into an in ltration product, and we develop various representations for the Newton transform of a language, together with concrete calculation rules for computing them.
Formal methods [FM]
Computer Security

Basold, H., Hansen, H., Pin, J.-É., & Rutten, J. (2015). Newton series, coinductively. Formal methods [FM]. CWI. doi:10.1007/978-3-319-25150-9_7