We present a general framework for the formal speci cation and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamical laws. For veri cation purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an in nite state space. The procedures iteratively compute state sets that are de nable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.
A time-synchronized system can be modeled as a hybrid system REF .
The Algorithmic Analysis of Hybrid Systems
Theoretical Computer Science
Mathematics Computer Science