of real-time systems whose correctness depends on relative magnitudes of different delays. Consequently, timed automata [7] were introduced as a formal notation to model the behavior of real-time systems. Its definition provides a simple way to annotate state-transition graphs with timing constraints

A hybrid automaton is a formal model for a mixed discrete-continuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discrete-continuous state spaces that was previously studied

Conventional type systems specify interfaces in terms of values and domains.

We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many

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Suppose one is given a description of a system, together with an observation of the system's behaviour which conflicts with the way the system is meant to behave. The diagnostic problem is to determine those components of the system which, when assumed to be functioning abnormally, will explain the discrepancy between the observed and correct system behaviour. We propose a general theory for this problem. The theory requires only that the system be described in a suitable logic. Moreover, there are many such suitable logics, e.g. first-order, temporal, dynamic, etc. As a result, the theory accommodates diagnostic reasoning in a wide variety of practical settings, including digital and analogue circuits, medicine, and database updates. The theory leads to an algorithm for computing all diagnoses, and to various results concerning principles of measurement for discriminating among competing diagnoses. Finally, the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning.

All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based

We describe finite-state programs over real-numbered time in a guarded-command language with real-valued clocks or, equivalently, as finite automata with real-valued clocks. Model checking answers the question which states of a real-time program satisfy a branching-time specification (given

Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general

Traditionally, virtual reality systems use 3D computer graphics to model and render virtual environments in real-time. This approach usually requires laborious modeling and expensive special purpose rendering hardware. The rendering quality and scene complexity are often limited because of the real-time