Forecasting black holes in abstract geometrical computation is highly unpredictable

  • Authors:

  • Jérôme Durand-Lose

  • Affiliations:

  • Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, ORL ANS Cedex 2

  • Venue:
  • TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
  • Year:
  • 2006

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Abstract

In Abstract geometrical computation for black hole computation (MCU ’04, LNCS 3354), the author provides a setting based on rational numbers, abstract geometrical computation, with super-Turing capability: any recursively enumerable set can be decided in finite time. To achieve this, a Zeno-like construction is used to provide an accumulation similar in effect to the black holes of the black hole model. We prove here that forecasting an accumulation is Σ$_{\rm 2}^{\rm 0}$-complete (in the arithmetical hierarchy) even if only energy conserving signal machines are addressed (as in the cited paper). The Σ$_{\rm 2}^{\rm 0}$-hardness is achieved by reducing the problem of deciding whether a recursive function (represented by a 2-counter automaton) is strictly partial. The Σ$_{\rm 2}^{\rm 0}$-membership is proved with a logical characterization.