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Finite Bisimulations for Dynamical Systems with Overlapping Trajectories

Authors Béatrice Bérard, Patricia Bouyer, Vincent Jugé



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Author Details

Béatrice Bérard
  • Sorbonne Université, CNRS, Laboratoire d'Informatique de Paris 6, LIP6, F-75005 Paris, France
Patricia Bouyer
  • LSV, CNRS, ENS Paris-Saclay, Univ. Paris-Saclay, France
Vincent Jugé
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE, UPEM, F-77454, Marne-la-Vallée, France

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Béatrice Bérard, Patricia Bouyer, and Vincent Jugé. Finite Bisimulations for Dynamical Systems with Overlapping Trajectories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 26:1-26:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CSL.2018.26

Abstract

Having a finite bisimulation is a good feature for a dynamical system, since it can lead to the decidability of the verification of reachability properties. We investigate a new class of o-minimal dynamical systems with very general flows, where the classical restrictions on trajectory intersections are partly lifted. We identify conditions, that we call Finite and Uniform Crossing: When Finite Crossing holds, the time-abstract bisimulation is computable and, under the stronger Uniform Crossing assumption, this bisimulation is finite and definable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Reachability properties
  • dynamical systems
  • o-minimal structures
  • intersecting trajectories
  • finite bisimulations

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