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Logical Analysis of Hybrid Systems

Proving Theorems for Complex Dynamics

  • Book
  • © 2010

Overview

Authors:
  1. André Platzer

    1. School of Computer Science, Carnegie Mellon University, Pittsburgh, USA

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  • A unique approach to hybrid systems verification
  • The first book that leverages the power of logic for hybrid systems
  • Intended for researchers, postgraduates, and professionals book
  • Includes supplementary material: sn.pub/extras

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxx
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  2. Introduction

    • André Platzer
    Pages 1-29

  3. Logics and Proof Calculi for Hybrid Systems

    1. Front Matter

      Pages 31-32
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    2. Differential Dynamic Logic dℒ

      • André Platzer
      Pages 33-122

    3. Differential-Algebraic Dynamic Logic DAL

      • André Platzer
      Pages 123-202

    4. Differential Temporal Dynamic Logic dTL

      • André Platzer
      Pages 203-230

  4. Automated Theorem Proving for Hybrid Systems

    1. Front Matter

      Pages 231-232
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    2. Deduction Modulo Real Algebra and Computer Algebra

      • André Platzer
      Pages 233-252

    3. Computing Differential Invariants as Fixed Points

      • André Platzer
      Pages 253-274

  5. Case Studies and Applications in Hybrid Systems Verification

    1. Front Matter

      Pages 275-276
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    2. European Train Control System

      • André Platzer
      Pages 277-301

    3. Air Traffic Collision Avoidance

      • André Platzer
      Pages 303-334

    4. Conclusion

      • André Platzer
      Pages 335-338

  6. Back Matter

    Pages 339-426
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Keywords

About this book

Hybrid systems are models for complex physical systems and have become a widely used concept for understanding their behavior. Many applications are safety-critical, including car, railway, and air traffic control, robotics, physical–chemical process control, and biomedical devices. Hybrid systems analysis studies how we can build computerized controllers for physical systems which are guaranteed to meet their design goals. The author gives a unique, logic-based perspective on hybrid systems analysis. It is the first book that leverages the power of logic for hybrid systems. The author develops a coherent logical approach for systematic hybrid systems analysis, covering its theory, practice, and applications. It is further shown how the developed verification techniques can be used to study air traffic and railway control systems. This book is intended for researchers, postgraduates, and professionals who are interested in hybrid systems analysis, cyberphysical or embedded systems design, logic and theorem proving, or transportation and automation.

Reviews

"This book offers a truly unique approach to hybrid systems verification with logic and theorem proving." (Edmund M. Clarke, Carnegie Mellon University)

Authors and Affiliations

  • School of Computer Science, Carnegie Mellon University, Pittsburgh, USA

    André Platzer

About the author

The author is an assistant professor in the Computer Science Department at Carnegie Mellon University. He has an M.Sc. in computer science from the University of Karlsruhe, Germany and a Ph.D. in computer science from the University of Oldenburg, Germany. Among other awards he won best paper awards at the Tableaux 2007 and FM 2009 conferences, he was among Popular Science Magazine's annual "Brilliant 10" in 2009, he received the ACM Doctoral Dissertation Honorable Mention Award in 2009, he was among the IEEE Intelligent Systems' biennial "AI's 10 to Watch" in 2011, and he received an NSF Career award in 2011. His research interests include the logical foundations of cyberphysical systems, theorem proving and model checking.

 

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