InforLorV4, Main, Exploration, bibRecord, 001089

Computation with perturbed dynamical systems

Identifieur interne : 001089 ( Main/Exploration ); précédent : 001088; suivant : 001090

Computation with perturbed dynamical systems

Auteurs : Olivier Bournez [France] ; Daniel Graça [Portugal] ; Emmanuel Hainry [France]

Source :

Journal of Computer and System Sciences [ 0022-0000 ] ; 2013-08.

RBID : Hal:hal-00643634

English descriptors

mix :
- Dynamical systems, computational power, reachability, robustness, verification.

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.

Url:

https://hal.inria.fr/hal-00643634

DOI: 10.1016/j.jcss.2013.01.025

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 001737
to stream Hal, to step Curation: 001737
to stream Hal, to step Checkpoint: 000F99
to stream Main, to step Merge: 001100
to stream Main, to step Curation: 001089

Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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Computation with perturbed dynamical systems

Computation with perturbed dynamical systems

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