## Hybrid Automata with Finite Bisimulations (1995)

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@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...

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Citation Context ... important for the analysis of embedded systems, because the problems of language emptiness, model checking, and controller synthesis are decidable for hybrid automata that are finitary and effective =-=[1, 13, 19]. There ha-=-ve been several results of the type "the emptiness problem is undecidable for hybrid automata with clocks and a stopwatch" [2, 12, 15]. While these results leave little hope for finding A pr... |

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Citation Context ... important for the analysis of embedded systems, because the problems of language emptiness, model checking, and controller synthesis are decidable for hybrid automata that are finitary and effective =-=[1, 13, 19]. There ha-=-ve been several results of the type "the emptiness problem is undecidable for hybrid automata with clocks and a stopwatch" [2, 12, 15]. While these results leave little hope for finding A pr... |

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Citation Context ... bisimulation. 1 Introduction A hybrid automaton [2] is a mathematical model for a digital program that interacts with an analog environment. Hybrid automata are useful for analyzing embedded systems =-=[4, 10, 14, 21, 22]-=-. We advocate the view of hybrid automata as infinite-state transition systems. We call an infinitestate transition system finitary and effective if it has a finite bisimulation that can be constructe... |

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Citation Context ... computable if A is effective. The successive approximation converges ---i.e., the procedure BisimApprox terminates--- iff A is finitary. Implementations of the procedure BisimApprox are discussed in =-=[16, 23]-=- for finite automata and in [7, 17] for arbitrary transition systems. Questions about transition systems. 1 The emptiness problem for transition systems asks, given a transition system A, is the langu... |

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Citation Context ...cessary for decidability. In particular, hybrid automata with infinite 1-counter encodable bisimulations are decidable, because emptiness can be reduced to the emptiness problem for pushdown automata =-=[8]-=-. Examples of such automata include 2D grid automata with the slope set S 2 and only one bounded variable (see full paper). Second, we expect that our phase view of hybrid systems will also lead to a ... |

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Citation Context ... computable if A is effective. The successive approximation converges ---i.e., the procedure BisimApprox terminates--- iff A is finitary. Implementations of the procedure BisimApprox are discussed in =-=[16, 23]-=- for finite automata and in [7, 17] for arbitrary transition systems. Questions about transition systems. 1 The emptiness problem for transition systems asks, given a transition system A, is the langu... |

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3 | Three partition-re nement algorithms - Paige, Tarjan - 1987 |

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1 | Verifying!-regular properties for subclasses of linear hybrid systems. Computer-aided Veri cation - Bouajjani, Robbana - 1995 |