Affiliation:
1. Department of Mathematics, University of Wales SwanseaSingleton Park, Swansea SA3 2HN, UK
2. Department of Computer Science, University of Wales SwanseaSingleton Park, Swansea SA3 2HN, UK
Abstract
Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a three-dimensional Newtonian machine which given
any
point
x
∈[0, 1] can generate an infinite sequence [
p
n
,
q
n
], for
n
=1, 2, …, of rational number interval approximations, that converges to
x
as
n
→∞. The machine is a system for scattering and collecting particles. The theorem implies that every point x∈[0, 1] is computable by a simple Newtonian kinematic system that is bounded in space and mass and for which the calculation of the nth approximation of x takes place in
O
(
n
) time with
O
(
n
) energy. We describe variants of the scatter machine which explain why our machine is non-deterministic.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference45 articles.
1. Beggs E. J. & Tucker J. V. 2004 Computations via experiments with kinematic systems. Research Report no. 4.04 Department of Mathematics University of Wales Swansea or Technical Report no. 5-2004 Department of Computer Science University of Wales Swansea.
2. Embedding infinitely parallel computation in Newtonian kinematics;Beggs E.J;Appl. Math. Comput,2006
3. Can Newtonian systems, bounded in space, time, mass and energy compute all functions?
4. Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
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