Reversible parallel computation: an evolving space-model
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Weakly computable real numbers
Journal of Complexity
Collision-based computing
Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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
Natural Computing: an international journal
Abstract geometrical computation 3: black holes for classical and analog computing
Natural Computing: an international journal
Transition Systems over Continuous Time-Space
Electronic Notes in Theoretical Computer Science (ENTCS)
A computability theory of real numbers
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
UC'05 Proceedings of the 4th international conference on Unconventional Computation
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 7: geometrical accumulations and computably enumerable real numbers
Natural Computing: an international journal
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Abstract geometrical computation involves drawing colored line segments (traces of signals) 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 be devised to unlimitedly accelerate a computation and provide, in a finite duration, exact analog values as limits. In the present paper, we show that starting with rational numbers for coordinates and speeds, the time of any accumulation is a c.e. (computably enumerable) real number and moreover, there is a signal machine and an initial configuration that accumulates at any c.e. time. Similarly, we show that the spatial positions of accumulations are exactly the dc. 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.