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Quantified Differential Dynamic Logic for Distributed Hybrid Systems

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Computer Science Logic (CSL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6247))

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Abstract

We address a fundamental mismatch between the combinations of dynamics that occur in complex physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic networks, where neither structure nor dimension stay the same while the system follows mixed discrete and continuous dynamics.

We provide the logical foundations for closing this analytic gap. We develop a system model for distributed hybrid systems that combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for it. We prove that this calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when new cars may appear dynamically on the road.

This material is based upon work supported by the National Science Foundation under Grant Nos. CNS-0926181 and CNS-0931985, by the NASA grant NNG-05GF84H, and by the ONR award N00014-10-1-0188.

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Author information

Authors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

    André Platzer

Authors
  1. André Platzer
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Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Formal Methods in Systems Engineering, Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Helmut Veith

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Platzer, A. (2010). Quantified Differential Dynamic Logic for Distributed Hybrid Systems. In: Dawar, A., Veith, H. (eds) Computer Science Logic. CSL 2010. Lecture Notes in Computer Science, vol 6247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15205-4_36

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  • DOI: https://doi.org/10.1007/978-3-642-15205-4_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15204-7

  • Online ISBN: 978-3-642-15205-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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