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)


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.


Hybrid System Transition System Integral Curve Open Domain Parameterized Class 
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© 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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