The real number model in numerical analysis
Journal of Complexity
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Complexity and real computation
Complexity and real computation
Computable analysis: an introduction
Computable analysis: an introduction
Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
A weak version of the Blum, Shub and Smale model
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Reversible conservative rational abstract geometrical computation is turing-universal
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of 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 for black hole computation
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Abstract Geometrical Computation and Computable Analysis
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
Geometrical accumulations and computably enumerable real numbers
UC'11 Proceedings of the 10th international conference on Unconventional computation
Abstract geometrical computation 7: geometrical accumulations and computably enumerable real numbers
Natural Computing: an international journal
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Abstract geometrical computation naturally arises as acontinuous counterpart of cellular automata. It relies on signals(dimensionless points) traveling at constant speed in a continuousspace in continuous time. When signals collide, they are replacedby new signals according to some collision rules. This simpledynamics relies on real numbers with exact precision and is alreadyknown to be able to carry out any (discrete) Turing-computation.The Blum, Shub and Small (BSS) model is famous for computing overℝ (considered here as a ℝ unlimited register machine)by performing algebraic computations.We prove that signal machines (set of signals and correspondingrules) and the infinite-dimension linear (multiplications are onlyby constants) BSS machines can simulate one another.