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Newton series, coinductively: a comparative study of composition
2017
Mathematical Structures in Computer Science
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
doi:10.1017/s0960129517000159
fatcat:4l6trke2hvethpppsdhnwps6py