Euclidian geometry in terms of automata theory
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A result about the power of geometric oracle machines
Theoretical Computer Science
Computable analysis: an introduction
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Weakly computable real numbers
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Collision-based computing
Abstract Geometrical Computation and the Linear Blum, Shub and Smale Model
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Abstract Geometrical Computation and Computable Analysis
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
General relativistic hypercomputing and foundation of mathematics
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Abstract geometrical computation 3: black holes for classical and analog computing
Natural Computing: an international journal
Transition Systems over Continuous Time-Space
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Geometrical accumulations and computably enumerable real numbers
UC'11 Proceedings of the 10th international conference on Unconventional computation
A computability theory of real numbers
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Forecasting black holes in abstract geometrical computation is highly unpredictable
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Abstract geometrical computation: turing-computing ability and undecidability
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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Using rules to automatically extend a drawing on an Euclidean space might lead to accumulating drawings into a single point. Such points are characterized in the context of Abstract geometrical computation. Colored line segments (traces of signals) are drawn according to rules: signals with similar color are parallel and when they intersect, they are replaced according to their colors. Time and space are continuous and accumulations can happen. Constructions exist to unboundedly accelerate a computation and provide, in a finite duration, exact analog values as limits/accumulations. Starting with rational numbers for coordinates and speeds, the time of any isolated accumulation is a c.e. (computably enumerable) real number. There is a signal machine and an initial configuration that accumulates at any c.e. time. Similarly, the spatial positions of isolated accumulations are exactly the d-c.e. (difference of computably enumerable) numbers. Moreover, there is a signal machine that can accumulate at any c.e. time or d-c.e. position depending only on the initial configuration. These existence results rely on a two-level construction: an inner structure simulates a Turing machine that output orders to the outer structure which handles the accumulation.