• Energy Research

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.

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.

Le modèle du calcul avec un trou noir fournit une puissance de calcul supérieure au calcul Turing classique puisqu'on peut y décider tout problème récursivement énumérable(R.E.). Dans cet article, nous proposons un modèle de calcul géométrique,conservative abstract geometrical computation,qui a la même propriété : il peut simuler n'importe quelle machine de Turing et, en créant une accumulation,décider n'importe quel problème R.E.Seulement un nombre fini de signaux peuvent quitter l'accumulation et il est possible de savoir si quoique ce soit l'a quitté. Ceci correspond à l'artefact du trou noir. The Black hole model of computation provides a computing power that goes beyond the classical Turing computability since it offers the possibility to decide in finite time any recursively enumerable (\RE) problem. In this article, we provide a geometric model of computation, conservative abstract geometrical computation, that has the same property: it can simulate any Turing machine and can decide any \RE 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 artifact.

Le modèle du calcul avec un trou noir fournit une puissance de calcul supérieure au calcul Turing classique puisqu'on peut y décider tout problème récursivement énumérable(R.E.). Dans cet article, nous proposons un modèle de calcul géométrique,conservative abstract geometrical computation,qui a la même propriété : il peut simuler n'importe quelle machine de Turing et, en créant une accumulation,décider n'importe quel problème R.E.Seulement un nombre fini de signaux peuvent quitter l'accumulation et il est possible de savoir si quoique ce soit l'a quitté. Ceci correspond à l'artefact du trou noir. The Black hole model of computation provides a computing power that goes beyond the classical Turing computability since it offers the possibility to decide in finite time any recursively enumerable (\RE) problem. In this article, we provide a geometric model of computation, conservative abstract geometrical computation, that has the same property: it can simulate any Turing machine and can decide any \RE 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 artifact.

In the context of Abstract geometrical computation, it has been proved that black hole model (and SAD computers) can be implemented. To be more physic-like, it would be interesting that the construction is reversible and preserves some energy. There is already a (energy) conservative and reversible two-counter automaton simulation. In the present paper, based on reversible and conservative stacks, reversible Turing machines are simulated. Then a shrinking construction that preserves these properties is presented. All together, a black hole model implementation that is reversible and conservative (both the shrinking structure and the universal Turing machine) is provided.

In the context of Abstract geometrical computation, it has been proved that black hole model (and SAD computers) can be implemented. To be more physic-like, it would be interesting that the construction is reversible and preserves some energy. There is already a (energy) conservative and reversible two-counter automaton simulation. In the present paper, based on reversible and conservative stacks, reversible Turing machines are simulated. Then a shrinking construction that preserves these properties is presented. All together, a black hole model implementation that is reversible and conservative (both the shrinking structure and the universal Turing machine) is provided.

In the context of Abstract geometrical computation, it has been proved that black hole model (and SAD computers) can be implemented. To be more physic-like, it would be interesting that the construction is reversible and preserves some energy. There is already a (energy) conservative and reversible two-counter automaton simulation. In the present paper, based on reversible and conservative stacks, reversible Turing machines are simulated. Then a shrinking construction that preserves these properties is presented. All together, a black hole model implementation that is reversible and conservative (both the shrinking structure and the universal Turing machine) is provided.