Summary: Modularity for Timed and Hybrid Systems ?;??
Rajeev Alur Thomas A. Henzinger
EECS Department, University of California, Berkeley, CA 94720­1770, U.S.A.
Email: falur,tahg@eecs.berkeley.edu
Abstract. In a trace­based 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 real­time 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 real­time 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 assume­guarantee principle for reasoning
about timed and hybrid modules, and a method for synthesizing receptive controllers of timed
and hybrid modules.
1 Introduction
Over the past decade, much research has focused on the modeling and verification of timed

Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania

Collections: Computer Technologies and Information Sciences