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Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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Abstract geometrical computation 4: Small Turing universal signal machines
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Reversible conservative rational abstract geometrical computation is turing-universal
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Forecasting black holes in abstract geometrical computation is highly unpredictable
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Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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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 ($\mathcal{R.E.}$) problem. In this paper, we provide a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can decide any $\mathcal{R.E.}$ 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.