Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

We study finite bisimulations of dynamical systems in Rn defined by Pfaffian maps. The pure existence of finite bisimulations for a more general class of o-minimal systems was shown in [2, 3, 12]. In [9] the authors proved a double exponential upper bound on the size of a bisimulation in terms of the size of description of the dynamical system. In the present paper we improve it to a single exponential upper bound, and show that this bound is tight, by exhibiting a parameterized class of systems on which it is attained.

• Type: Journal
• Year: 2008
• Where: MST
• Authors: Margarita V. Korovina, Nicolai Vorobjov
• Keywords: Dynamical System, Exponential Upper Bound, MST 2008, Pure Existence