Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

Korovina, Margarita and Nicolai, Vorobjov (2008) Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems. Theory of Computing Systems, 43 (3-4). pp. 498-515. ISSN 1432-4350

PDF jtcs_08_korvor.pdf Download (422kB)

Abstract

We study finite bisimulations of dynamical systems in ℝ n defined by Pfaffian maps. The pure existence of finite bisimulations for a more general class of o-minimal systems was shown in Brihaye et al. (Lecture Notes in Comput. Sci. 2993, 219–233, 2004), Davoren (Theor. Inf. Appl. 33(4/5), 357–382, 1999), Lafferriere et al. (Math. Control Signals Syst. 13, 1–21, 2000). In Lecture Notes in Comput. Sci. 3210, 2004, 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.

Item Type:	Article
Uncontrolled Keywords:	CICADA, Dynamical system, Hybrid system, Bisimulation,Semialgebraic geometry
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User:	Dr Margarita Korovina
Date Deposited:	08 Jan 2010
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1380

Actions (login required)

View Item