Modularity for Timed and Hybrid Systems
نویسندگان
چکیده
In a trace-based world, the modular specification, verification, and control of live systems require each module to be receptive; that is, each module must be able to meet its liveness assumptions no matter how the other modules behave. In a real-time world, liveness is automatically present in the form of diverging time. The receptiveness condition, then, translates to the requirement that a module must be able to let time diverge no matter how the environmentbehaves.We study the receptivenesscondition for real-time systemsby extending the model of reactive modules to timed and hybrid modules. We define the receptiveness of such a module as the existence of a winning strategy in a game of the module against its environment. By solving the game on region graphs, we present an (optimal) EXPTIME algorithm for checking the receptiveness of propositional timed modules. By giving a fixpoint characterization of the game, we present a symbolic procedure for checking the receptiveness of linear hybrid modules. Finally, we present an assume-guarantee principle for reasoning about timed and hybrid modules, and a method for synthesizing receptive controllers of timed and hybrid modules.
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