Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers

Issue title: SPECIAL ISSUE MCU2004

Article type: Research Article

Authors: Durand-Lose, Jérôme

Affiliations: Laboratoire d'Informatique Fondamentale d'Orléans, Université d'Orléans, B.P. 6759, F-45067 Orléans Cedex 2, France. E-mail: [email protected]

Abstract: The Black hole model of computation provides super-Turing computing power since it offers the possibility to decide in finite (observer's) time any recursively enumerable (R.E.) problem. In this paper, we provide a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers (and not real numbers), has the same property: it can simulate any Turing machine and can decide any R.E. problem through the creation of an accumulation. Finitely many signals can leave any accumulation, and it can be known whether anything leaves. This corresponds to a black hole effect.

Keywords: Abstract geometrical computation, Black hole model, Energy conservation, Malament-Hogarth space-time, Super-Turing computation, Turing universality, Zeno phenomena

Journal: Fundamenta Informaticae, vol. 74, no. 4, pp. 491-510, 2006