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Conference on Computability in Europe

CiE 2015: Evolving Computability pp 71–82Cite as

Newton’s Forward Difference Equation for Functions from Words to Words

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9136))

Abstract

Newton’s forward difference equation gives an expression of a function from \({\mathbb {N}}\) to \({\mathbb {Z}}\) in terms of the initial value of the function and the powers of the forward difference operator. An extension of this formula to functions from \(A^*\) to \({\mathbb {Z}}\) was given in 2008 by P. Silva and the author. In this paper, the formula is further extended to functions from \(A^*\) into the free group over \(B\).

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Notes

  1. 1.

    Therefore, the notation \(FG(M)\) and \(FG[M]\) refer to the same set, but to different structures: the free group on \(M\) in the first case, the free near semiring on \(M\) in the latter case.

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Acknowlegements

I would like to thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. LIAFA, Université Paris-Diderot and CNRS, Case 7014, 75205, Paris Cedex 13, France

    Jean-Éric Pin

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  1. Jean-Éric Pin
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Correspondence to Jean-Éric Pin .

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Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. University of Bucharest, Bucharest, Romania

    Victor Mitrana

  3. Sofia University, Sofia, Bulgaria

    Mariya Soskova

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Pin, JÉ. (2015). Newton’s Forward Difference Equation for Functions from Words to Words. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-20028-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20027-9

  • Online ISBN: 978-3-319-20028-6

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