The computational power of continuous dynamic systems

Authors:
Jerzy Mycka;José Félix Costa
Affiliations:
Institute of Mathematics, University of Maria Curie-Sklodowska, Lublin, Poland;Department of Mathematics, I.S.T., Universidade Técnica de Lisboa, Lisboa, Portugal
Venue:
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Year:
2004

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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.