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

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## 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 |
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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: | http://eprints.maths.manchester.ac.uk/id/eprint/1380 |

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