Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Almagor, Shaull; Kelmendi, Edon; Ouaknine, Joël; Worrell, James https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-125141
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Invariants for Continuous Linear Dynamical Systems

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Abstract

Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by synthesising inductive invariants. This is the task of finding a set of states that is closed under the dynamics of the system and is disjoint from a given set of error states. In this paper we study the problem of synthesising inductive invariants that are definable in o-minimal expansions of the ordered field of real numbers. In particular, assuming Schanuel’s conjecture in transcendental number theory, we establish effective synthesis of o-minimal invariants in the case of semi-algebraic error sets. Without using Schanuel’s conjecture, we give a procedure for synthesizing o-minimal invariants that contain all but a bounded initial segment of the orbit and are disjoint from a given semi-algebraic error set. We further prove that effective synthesis of semi-algebraic invariants that contain the whole orbit, is at least as hard as a certain open problem in transcendental number theory.

BibTeX - Entry

@InProceedings{almagor_et_al:LIPIcs:2020:12514,
  author =	{Shaull Almagor and Edon Kelmendi and Jo{\"e}l Ouaknine and James Worrell},
  title =	{{Invariants for Continuous Linear Dynamical Systems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{107:1--107:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12514},
  URN =		{urn:nbn:de:0030-drops-125141},
  doi =		{10.4230/LIPIcs.ICALP.2020.107},
  annote =	{Keywords: Invariants, continuous linear dynamical systems, continuous Skolem problem, safety, o-minimality}
}

Keywords: Invariants, continuous linear dynamical systems, continuous Skolem problem, safety, o-minimality
Seminar: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue date: 2020
Date of publication: 29.06.2020


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