@inbook{14df6edb554c4aac9bcb915dffed5642,

title = "Upper and lower bounds on sizes of finite bisimulations of Pfaffian hybrid systems",

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. [3,4,131). 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.",

author = "M Korovina and N Vorobjov",

note = "ID number: ISI:000239424100028",

year = "2006",

language = "English",

isbn = "0302-9743",

volume = "3988",

series = "Lecture Notes in Computer Science",

pages = "267--276",

booktitle = "Logical Approaches to Computational Barriers, Proceedings",

}