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

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. [2, 3, 11]). 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 [9] 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.

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Margarita V. Korovina, Nicolai Vorobjov
• Keywords: DAGSTUHL 2006, DAGSTUHL 2007, Dynamical Systems, Exponential Upper Bound, Finite Bisimulations