Creating and sharing knowledge for telecommunications

Computation with perturbed dynamical systems

Bournez, O. ; Graça, D. ; Hainry, E.

Journal of Computer and System Sciences Vol. 79, Nº 5, pp. 714 - 724, August, 2013.

ISSN (print): 0022-0000
ISSN (online):

Scimago Journal Ranking: (in )

Digital Object Identifier: 10.1016/j.jcss.2013.01.025

Download Full text PDF ( 325 KBs)

Abstract
This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability.