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Denmark A n E x t e n d e d D u r a t i o n Calculus for Hybrid Real-Time Systems Hansen, Universitiit Oldenburg and Teehn. Ravn, Technical University of Denmark M.R. Pnueli Weizmann Institute Verifying H y b r i d Systems Rischel, Technical University of Denmark Introduction Z. Grossman, University of Illinois at Chicago A. We gratefully acknowledge the financial support of the workshop in Lyngby granted by the Technical University of Denmark under the research programme 'Mathematical Modelling of Computer Based Systems'.ĭepartment of Computer Science Technical University of Denmark Lyngby, June 1993ĬONTENTS R.L.

We also wish to thank the following referees: H. We are very grateful to Albert Benveniste, Anil Nerode, Amir Pnueli and WillemPaul de Roever for their help in organizing this volume.

Some are invited papers from other researchers who were not able to attend the workshops. Some papers are the final versions of papers presented at these workshops. This volume of invited refereed papers is inspired by a workshop on the Theory of Hybrid Systems, held October 19-21, 1992 at the Technical University, Lyngby, Denmark, and by a prior Hybrid Systems Workshop, June 10-12, 1991 at the Mathematical Sciences Institute, Cornell University, USA, organized by R.L. 9 Springer-Verlag Berlin Heidelberg 1993 Printed in Germany Typesetting: Camera-ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. Violations are liable for prosecution under the German Copyright Law. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. All rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. ISBN 8-6 Springer-Verlag Berlin Heidelberg New York ISBN 8-6 Springer-Verlag New York Berlin Heidelberg

Volume Editors Robert Lee Grossman Department of Mathematics, Statistics & Computer Science University of Illinois at Chicago, Chicago, IL 60680, USA Anil Nerode Mathematical Science Institute, Comell University Ithaca, NY 14853, USA Anders Peter Ravn Hans Rischel Department of Computer Science,Technical University of Denmark DK-2800 Lyngby, DenmarkĬR Subject Classification (1991): C.l.m, C.3, D.2.1, F.3.1, F.1-2 Juris Hartmanis Cornell University Department of Computer Science 4130 Upson Hall Ithaca, NY 14853, USA

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Series Editors Gerhard Goos Universit~it Karlsruhe Postfach 69 80 Vincenz-Priessnitz- StraSe 1 D-76131 Karlsruhe, Germany Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest Grossman Anil Nerode Anders E Ravn Hans Rischel (Eds.) Lecture Notes in Computer Science Edited by G. Some papers are the final versions of papers presented at these workshops and some are invited papers from other researchers who were not able to attend these workshops. This volume of invited refereed papers is inspired by a workshop on the Theory of Hybrid Systems, held at the Technical University, Lyngby, Denmark, in October 1992, and by a prior Hybrid Systems Workshop, held at Cornell University, USA, in June 1991, organized by R.L. The identifying characteristic of hybrid systems is that they incorporate both continuous components governed by differential equations and also digital components - digital computers, sensors, and actuators controlled by programs.

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Control systems for inherently unstable aircraft and computer aided manufacturing are typical applications for hybrid systems, but due to the rapid development of processor and circuit technology modern cars and consumer electronics use software to control physical processes. Hybrid systems are networks of interacting digital and analog devices.

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