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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 1996: SOFSEM'96: Theory and Practice of Informatics pp 335–342Cite as

Feasible real random access machines

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1175))

Abstract

We present a modified real RAM model which is equipped with the usual discrete and real-valued arithmetic operations and with a finite precision test <k which allows comparisons of real numbers only up to a variable uncertainty 1/k+1 Furthermore our feasible RAM has an extended semantics which allows approximative computations. Using a logarithmic complexity measure we prove that all functions computable on a feasible RAM in time O(t) can be computed on a Turing machine in time O(t 2 · log(t) · log log (t)). Vice versa all functions computable on a Turing machine in time O(t) are computable on a feasible RAM in time O(t). Thus our real RAM model does not only express exactly the computational power of Turing machines on real numbers (in the sense of Grzegorczyk), but it also yields a high-level tool for realistic time complexity estimations on real numbers.

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Authors and Affiliations

  1. Theoretische Informatik I, FernUniversität Hagen, D-58084, Hagen, Germany

    Vasco Brattka & Peter Hertling

Authors
  1. Vasco Brattka
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  2. Peter Hertling
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Editor information

Keith G. Jeffery Jaroslav Král Miroslav Bartošek

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© 1996 Springer-Verlag Berlin Heidelberg

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Brattka, V., Hertling, P. (1996). Feasible real random access machines. In: Jeffery, K.G., Král, J., Bartošek, M. (eds) SOFSEM'96: Theory and Practice of Informatics. SOFSEM 1996. Lecture Notes in Computer Science, vol 1175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037415

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  • DOI: https://doi.org/10.1007/BFb0037415

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61994-9

  • Online ISBN: 978-3-540-49588-8

  • eBook Packages: Springer Book Archive

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