 
Summary: The Algorithmic Analysis of Hybrid Systems \Lambda
R. Alur y C. Courcoubetis z N. Halbwachs x T.A. Henzinger  P.H. Ho x
X. Nicollin z A. Olivero z J. Sifakis z S. Yovine z
Abstract
We present a general framework for the formal specification and algorithmic analysis of hybrid
systems. A hybrid system consists of a discrete program with an analog environment. We model
hybrid systems as finite automata equipped with variables that evolve continuously with time
according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid
systems, where all variables follow piecewiselinear trajectories. We provide decidability and
undecidability results for classes of linear hybrid systems, and we show that standard program
analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic
modelchecking and minimization procedures that are based on the reachability analysis of an
infinite state space. The procedures iteratively compute state sets that are definable 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.
\Lambda A preliminary version of this paper appeared in the Proceedings of the 11th International Conference on Analysis
and Optimization of Discrete Event Systems, Lecture Notes in Control and Information Sciences 199, SpringerVerlag,
1994, pp. 331351, and an extended version appeared in Theoretical Computer Science 138, 1995, pp. 334.
y AT&T Bell Laboratories, Murray Hill, NJ, U.S.A.
z University of Crete and ICS, FORTH, Heraklion, Greece. Partially supported by EspritBRA 6021 REACTP.
