Coupled map lattices as computational systems |
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| Authors: | Holden A V Tucker J V Zhang H Poole M J |
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| Institution: | Department of Physiology, University of Leeds, Leeds LS2 9JT, United KingdomDepartment of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, United KingdomDepartment of Physiology, University of Leeds, Leeds LS2 9JT, United KingdomDepartment of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, United Kingdom. |
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| Abstract: | The coupled map lattice (CML) as a mathematical model for a computer is considered. Using the theory of synchronous concurrent algorithms, it is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers. The analysis is based on new general mathematical definitions of CMLs, and an axiomatic approach to determining which models of computation can be used to simulate CMLs. |
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