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We present a general framework for the formal speciication and algorithmic analysis of hybrid systems. A h ybrid system consists of a discrete program with an analog environment. We m o d e l h ybrid systems as nite automata equipped with variables that evolve c o n tinuously with time according to dynamical laws. For veriication purposes, we restrict(More)
LUSTRE is a synchronous data-flow language for programming systems which interact with their environments in real-time. After an informal presentation of the language, we describe its semantics by means of structural inference rules. Moreover, we show how to use this semantics in order to generate efficient sequential code, namely, a finite state automaton(More)
Invited Paper Twelve years ago, PROCEEDINGS OF THE IEEE devoted a special section to the synchronous languages. This paper discusses the improvements , difficulties, and successes that have occured with the synchronous languages since then. Today, synchronous languages have been established as a technology of choice for modeling, specifying , validating,(More)
We investigate the beneets of using a synchronous data-ow language for programming critical real-time systems. These beneets concern ergonomy | since the dataaow approach meets traditional description tools used in this domain |, and ability to support formal design and veriication methods. We show, on a simple example, how the language Lustre and its(More)
Linear Relation Analysis [CH78,Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening,(More)