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

  • Margarita Korovina
  • Nicolai Vorobjov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

In this paper we study a class of hybrid systems defined by Pfaffian maps. It is a sub-class of o-minimal hybrid 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. [3,4,13]). The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done in [10] 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.

Keywords

Hybrid System Transition System Integral Curve Open Domain Parameterized Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Margarita Korovina
    • 1
    • 2
  • Nicolai Vorobjov
    • 3
  1. 1.Fachbereich Mathematik, Theoretische InformatikUniversität SiegenGermany
  2. 2.IIS SB RASNovosibirskRussia
  3. 3.Department of Computer ScienceUniversity of BathBathEngland

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