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Conference Papers Year : 2006

Forcasting Black Holes in Abstract geometrical computation is Highly Unpredictable

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 $\Sigma_2^0$-complete (in the arithmetical hierarchy) even if only energy conserving signal machines are addressed (as in the cited paper). The $\Sigma_2^0$-hardness is achieved by reducing the problem of deciding whether a recursive function (represented by a 2-counter automaton) is strictly partial. The $\Sigma_2^0$-membership is proved with a logical characterization.

Dates and versions

hal-00079692 , version 1 (13-06-2006)

Identifiers

Cite

Jérôme Durand-Lose. Forcasting Black Holes in Abstract geometrical computation is Highly Unpredictable. Theory and Appliacations of Models of Computations (TAMC~'06), 2006, France. pp.644-653, ⟨10.1007/11750321_61⟩. ⟨hal-00079692⟩
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