Upper and lower bounds on sizes of finite bisimulations of Pfaffian hybrid systems


Korovina, M. and Vorobjov, N., 2006. Upper and lower bounds on sizes of finite bisimulations of Pfaffian hybrid systems. In: Logical Approaches to Computational Barriers, Proceedings. Vol. 3988. , pp. 267-276. (Lecture Notes in Computer Science)

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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.


Item Type Book Sections
CreatorsKorovina, M.and Vorobjov, N.
DepartmentsFaculty of Science > Computer Science
ID Code5340
Additional InformationID number: ISI:000239424100028


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