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Geometrical Accumulations and Computably Enumerable Real Numbers

  • Jérôme Durand-Lose
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)

Abstract

Abstract geometrical computation involves drawing colored line segments (traces of signals) according to rules: signals with similar color are parallel and when they intersect, they are replaced according to their colors. Time and space are continuous and accumulations can be devised to unlimitedly accelerate a computation and provide, in a finite duration, exact analog values as limits.

In the present paper, we show that starting with rational numbers for coordinates and speeds, the time of any accumulation is a c.e. (computably enumerable) real number and moreover, there is a signal machine and an initial configuration that accumulates at any c.e. time. Similarly, we show that the spatial positions of accumulations are exactly the d-c.e. (difference of computably enumerable) numbers. Moreover, there is a signal machine that can accumulate at any c.e. time or d-c.e. position.

Keywords

Abstract geometrical computations Computable analysis Geometrical accumulations c.e. and d-c.e. real numbers Signal machine 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jérôme Durand-Lose
    • 1
  1. 1.LIFOUniversité d’OrléansORLÉANS Cedex 2

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