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Korovina, Margarita ; Vorobjov, Nicolai

Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

06021.KorovinaMargarita.Paper.713.pdf (0.2 MB)


In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors; see e.g. Brihaye et al (2004), Davoren (1999), Lafferriere et al (2000). The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done by Korovina et al (2004) where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained. The bounds provide a basis for designing efficient algorithms for computing bisimulations, solving reachability and motion planning problems.

BibTeX - Entry

  author =	{Margarita Korovina and Nicolai Vorobjov},
  title =	{Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems},
  booktitle =	{Reliable Implementation of Real Number Algorithms: Theory and Practice},
  year =	{2006},
  editor =	{Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
  number =	{06021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Hybrid systems,  Pfaffian functions, bisimulation}

Keywords: Hybrid systems, Pfaffian functions, bisimulation
Seminar: 06021 - Reliable Implementation of Real Number Algorithms: Theory and Practice
Issue Date: 2006
Date of publication: 13.09.2006

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