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Abstract: We show closed-form analytic functions consisting of a nite number of trigonometric terms can simulate Turing machines, with exponential slowdown in one dimension or in real time in two or more. (Update)
Context of citations to this paper: More
...is undecidable in dimension 2. In dimension one the known undecidable discrete time systems involve rather complex dynamics, e.g. in [26] an elementary function (a combination of sines an cosines) that simulates Turing machines (TM) with an exponential slowdown is...
.... that Turing machines (TMs) can be simulated by dynamical systems with piecewise arline functions (in three dimensional spaces) In [93], two elementary functions were constructed that simulates TMs. See reference therein for other undecidability results. Among other...
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BibTeX entry: (Update)
P. Koiran and C. Moore, "Closed-form analytic maps in one and two dimensions can simulate universal turing machines." To appear in Theoretical Computer Science. http://citeseer.ist.psu.edu/koiran99closedform.html More
@article{ koiran99closedform,
author = "Pascal Koiran and Cristopher Moore",
title = "Closed-form analytic maps in one and two dimensions can simulate universal {Turing} machines",
journal = "Theoretical Computer Science",
volume = "210",
number = "1",
pages = "217--223",
year = "1999",
url = "citeseer.ist.psu.edu/koiran99closedform.html" }
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