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.
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https://hal.archives-ouvertes.fr/hal-00079692
Contributor : Jérôme Durand-Lose <>
Submitted on : Tuesday, June 13, 2006 - 2:25:22 PM
Last modification on : Thursday, January 17, 2019 - 3:06:06 PM

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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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