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Decidability and Undecidability in Dynamical Systems

Identifieur interne : 003E07 ( Main/Merge ); précédent : 003E06; suivant : 003E08

Decidability and Undecidability in Dynamical Systems

Auteurs : Emmanuel Hainry [France]

Source :

RBID : Hal:inria-00429965

English descriptors

mix :
- Skolem-Pisot problem, dynamical systems, general purpose analog computer, reachability.

Abstract

A computing system can be modelized in various ways: one being in analogy with transfer functions, this is a function that associates to an input and optionally some internal states, an output ; another being focused on the behaviour of the system, that is describing the sequence of states the system will follow to get from this input to produce the output. This second kind of system can be defined by dynamical systems. They indeed describe the ``local'' behaviour of a system by associating a configuration of the system to the next configuration. It is obviously interesting to get an idea of the ``global'' behaviour of such a dynamical system. The questions that it raises can be for example related to the reachability of a certain configuration or set of configurations or to the computation of the points that will be visited infinitely often. Those questions are unfortunately very complex: they are in most cases undecidable. This article will describe the fundamental problems on dynamical systems and exhibit some results on decidability and undecidability in various kinds of dynamical systems.

Url:

https://hal.inria.fr/inria-00429965

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to stream Hal, to step Corpus: 001A83
to stream Hal, to step Curation: 001A83
to stream Hal, to step Checkpoint: 002F71

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Hal:inria-00429965

Le document en format XML

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<front><div type="abstract" xml:lang="en">A computing system can be modelized in various ways: one being in analogy with transfer functions, this is a function that associates to an input and optionally some internal states, an output ; another being focused on the behaviour of the system, that is describing the sequence of states the system will follow to get from this input to produce the output. This second kind of system can be defined by dynamical systems. They indeed describe the ``local'' behaviour of a system by associating a configuration of the system to the next configuration. It is obviously interesting to get an idea of the ``global'' behaviour of such a dynamical system. The questions that it raises can be for example related to the reachability of a certain configuration or set of configurations or to the computation of the points that will be visited infinitely often. Those questions are unfortunately very complex: they are in most cases undecidable. This article will describe the fundamental problems on dynamical systems and exhibit some results on decidability and undecidability in various kinds of dynamical systems.</div>
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Decidability and Undecidability in Dynamical Systems

Decidability and Undecidability in Dynamical Systems

Source :

English descriptors

Abstract

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

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri