## Hybrid Automata with Finite Bisimulations (1995)

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### BibTeX

@INPROCEEDINGS{Henzinger95hybridautomata,

author = {Thomas A. Henzinger},

title = {Hybrid Automata with Finite Bisimulations},

booktitle = {},

year = {1995},

pages = {324--335},

publisher = {Springer-Verlag}

}

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### Abstract

. The analysis, verification, and control of hybrid automata with finite bisimulations can be reduced to finite-state problems. We advocate a time-abstract, phasebased methodology for checking if a given hybrid automaton has a finite bisimulation. First, we factor the automaton into two components, a boolean automaton with a discrete dynamics on the finite state space B m and a euclidean automaton with a continuous dynamics on the infinite state space R n . Second, we investigate the phase portrait of the euclidean component. In this fashion, we obtain new decidability results for hybrid systems as well as new, uniform proofs of known decidability results. For example, we prove that if two hybrid automata have finite bisimulations, and both can be calibrated to a common time scale, then their product also has a finite bisimulation. 1 Introduction A hybrid automaton [2] is a mathematical model for a digital program that interacts with an analog environment. Hybrid automata are usef...