International Conference on Machines, Computations, and Universality

MCU 2004: Machines, Computations, and Universality pp 164-175

The Computational Power of Continuous Dynamic Systems

  • Jerzy Mycka
  • José Félix Costa
Conference paper

DOI: 10.1007/978-3-540-31834-7_13

Volume 3354 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Mycka J., Costa J.F. (2005) The Computational Power of Continuous Dynamic Systems. In: Margenstern M. (eds) Machines, Computations, and Universality. MCU 2004. Lecture Notes in Computer Science, vol 3354. Springer, Berlin, Heidelberg

Abstract

In this paper we show how to explore the classical theory of computability using the tools of Analysis: a differential scheme is substituted for the classical recurrence scheme and a limit operator is substituted for the classical minimalization. We show that most relevant problems of computability over the non negative integers can be dealt with over the reals: elementary functions are computable, Turing machines can be simulated, the hierarchy of non computable functions be represented (being the classical halting problem solvable in some level). The most typical concepts in Analysis become natural in this framework.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jerzy Mycka
    • 1
  • José Félix Costa
    • 2
  1. 1.Institute of MathematicsUniversity of Maria Curie-SklodowskaLublinPoland
  2. 2.Department of Mathematics, I.S.T.Universidade Técnica de LisboaLisboaPortugal