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Polynomial Time Computation in the Context of Recursive Analysis

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Book cover Foundational and Practical Aspects of Resource Analysis (FOPARA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6324))

Abstract

Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955] as an approach for investigating computation over the real numbers. It is based on enhancing the Turing machine model by introducing oracles that allow the machine to access finitary portions of the real infinite objects. Classes of computable real functions have been extensively studied as well as complexity-theoretic classes of functions restricted to compact domains. However, much less have been done regarding complexity of arbitrary real functions. In this article we give a definition of polynomial time computability of arbitrary real functions. Then we present two main applications based on that definition. The first one, which has already been published, concerns the relationships between polynomial time real computability and the corresponding notion over continuous rational functions. The second application, which is a new contribution to this article, concerns the construction of a function algebra that captures polynomial time real computability.

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Author information

Authors and Affiliations

  1. INRIA Nancy Grand-Est Research Centre, France

    Walid Gomaa

  2. Faculty of Engineering, Alexandria University, Alexandria, Egypt

    Walid Gomaa

Authors
  1. Walid Gomaa
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Editors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud Universiteit Nijmegen, P.O. Box 9102, 6500 HC, Nijmegen, The Netherlands

    Marko van Eekelen

  2. Institute for Computing and Information Sciences, Radboud University Nijmegen, The Netherlands

    Olha Shkaravska

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Gomaa, W. (2010). Polynomial Time Computation in the Context of Recursive Analysis. In: van Eekelen, M., Shkaravska, O. (eds) Foundational and Practical Aspects of Resource Analysis. FOPARA 2009. Lecture Notes in Computer Science, vol 6324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15331-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-15331-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15330-3

  • Online ISBN: 978-3-642-15331-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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