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Upper and Lower Bounds on Continuous-Time Computation

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Unconventional Models of Computation, UMC’2K

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

We consider various extensions and modifications of Shannon’s General Purpose Analog Computer, which is a model of computation by differential equations in continuous time. We show that several classical computation classes have natural analog counterparts, including the primitive recursive functions, the elementary functions, the levels of the Grzegorczyk hierarchy, and the arithmetical and analytical hierarchies.

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Author information

Authors and Affiliations

  1. D.M./I.S.A, Universidade Técnica de Usboa, Tapada da Ajuda, Lisboa, Portugal

    Manuel Lameiras Campagnolo

  2. Computer Science Department, University of New Mexico, Albuquerque, USA

    Cristopher Moore

  3. Physics and Astronomy Department, University of New Mexico, Albuquerque, USA

    Cristopher Moore

  4. Santa Fe Institute, Santa Fe, USA

    Cristopher Moore

Authors
  1. Manuel Lameiras Campagnolo
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  2. Cristopher Moore
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Editor information

Editors and Affiliations

  1. Solvay Institutes, Free University of Brussels, Belgium

    I. Antoniou

  2. Department of Computer Science, University of Auckland, Auckland, New Zealand

    C. S. Calude  & M. J. Dinneen  & 

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© 2001 Springer-Verlag London

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Campagnolo, M.L., Moore, C. (2001). Upper and Lower Bounds on Continuous-Time Computation. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_12

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  • DOI: https://doi.org/10.1007/978-1-4471-0313-4_12

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-415-4

  • Online ISBN: 978-1-4471-0313-4

  • eBook Packages: Springer Book Archive

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