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.
Original language | English |
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Pages (from-to) | 498-515 |
Number of pages | 18 |
Journal | Theory of Computing Systems |
Volume | 43 |
Issue number | 3-4 |
Early online date | 3 Jul 2007 |
DOIs | |
Publication status | Published - 1 Dec 2008 |
Event | 2nd Conference on Computability in Europe - Swansea University, Department of Computer Science, Swansea, Wales, UK United Kingdom Duration: 30 Jun 2006 → 5 Jul 2006 |
Keywords
- Hybrid system
- Dynamical system
- Semialgebraic geometry
- Bisimulation