Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines

Graça, Daniel; Zhong, Ning

http://hdl.handle.net/10400.1/18414

Utilize este identificador para referenciar este registo.

Nome:	Descrição:	Tamanho:	Formato:
70287 (1).pdf		519.39 KB	Adobe PDF	Ver/Abrir

Contacte-nos

Autores

Graça, Daniel

Zhong, Ning

Resumo(s)

In this paper, we analyze the problem of finding the minimum dimension n such that an analytic map/ordinary differential equation over R n can simulate a Turing machine in a way that is robust to perturbations. We show that one-dimensional analytic maps are sufficient to robustly simulate Turing machines; but the minimum dimension for the analytic ordinary differential equations to robustly simulate Turing machines is two, under some reasonable assumptions. We also show that any Turing machine can be simulated by a two-dimensional C ∞ ordinary differential equation on the compact sphere S 2.