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


Reference:

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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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.

Details

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

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