The Orbit Problem for Parametric Linear Dynamical Systems

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Abstract

We study a parametric version of the Kannan-Lipton Orbit Problem for linear dynamical systems. We show decidability in the case of one parameter and Skolem-hardness with two or more parameters.
More precisely, consider a d-dimensional square matrix M whose entries are algebraic functions in one or more real variables. Given initial and target vectors u,v ∈ ℚd, the parametric point-to-point orbit problem asks whether there exist values of the parameters giving rise to a concrete matrix N ∈ ℝd×d, and a positive integer n ∈ ℕ, such that Nn u = v.
We show decidability for the case in which M depends only upon a single parameter, and we exhibit a reduction from the well-known Skolem Problem for linear recurrence sequences, suggesting intractability in the case of two or more parameters.

Details

Original languageEnglish
Title of host publication32nd International Conference on Concurrency Theory
EditorsSerge Haddad, Daniele Varacca
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages1-17
ISBN (electronic)9783959772037
ISBN (print)978-3-95977-203-7
Publication statusPublished - 2021
Peer-reviewedNo

Publication series

Series32nd International Conference on Concurrency Theory (CONCUR 2021) ; Vol. 203
Volume203
ISSN1868-8969

Conference

Title32nd International Conference on Concurrency Theory
Abbreviated titleCONCUR 2021
Duration23 - 27 August 2021
Website
Degree of recognitionInternational event
Locationonline
CityParis
CountryFrance

External IDs

ORCID /0000-0002-5321-9343/work/142236686
Scopus 85115337111

Keywords

DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis

ASJC Scopus subject areas

Keywords

  • Orbit problem, linear dynamical systems, parametric