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Polynomially Time Computable Functions over p-Adic Fields

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Computability and Complexity in Analysis (CCA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2064))

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Abstract

Based on the notion of a computable p-adic number the notion of a polynomially time computable function over the field of p-adic numbers is introduced and studied. Theorems relating analytical properties with computability properties are established. The complexity of roots, and inverse function theorems are established at the level of polynomial time complexity. Relations between differentiability and polynomial time complexity and the maximization problem are discussed. Differences and similarities between the analogous questions for the real numbers are pointed out.

The author expresses his acknowledgements to the helpful comments of the two anonymous referees.

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Authors and Affiliations

    Authors
    1. George Kapoulas
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    Editors and Affiliations

    1. University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK

      Jens Blanck

    2. Informatikzentrum, FernUniversität Hagen, 58084, Hagen, Germany

      Vasco Brattka  & Peter Hertling  & 

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    © 2001 Springer-Verlag Berlin Heidelberg

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    Kapoulas, G. (2001). Polynomially Time Computable Functions over p-Adic Fields. In: Blanck, J., Brattka, V., Hertling, P. (eds) Computability and Complexity in Analysis. CCA 2000. Lecture Notes in Computer Science, vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45335-0_8

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    • DOI: https://doi.org/10.1007/3-540-45335-0_8

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-42197-9

    • Online ISBN: 978-3-540-45335-2

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