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A Temporal Dynamic Logic for Verifying Hybrid System Invariants

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Logical Foundations of Computer Science (LFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4514))

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Abstract

We combine first-order dynamic logic for reasoning about possible behaviour of hybrid systems with temporal logic for reasoning about the temporal behaviour during their operation. Our logic supports verification of hybrid programs with first-order definable flows and provides a uniform treatment of discrete and continuous evolution. For our combined logic, we generalise the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of dynamic logic. On this basis, we provide a modular verification calculus that reduces correctness of temporal behaviour of hybrid systems to non-temporal reasoning. Using this calculus, we analyse safety invariants in a train control system and symbolically synthesise parametric safety constraints.

This research was supported by a fellowship of the German Academic Exchange Service (DAAD). It was also sponsored by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS, see www.avacs.org ).

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Authors and Affiliations

  1. University of Oldenburg, Department of Computing Science, Germany, Carnegie Mellon University, Computer Science Department, Pittsburgh, PA,  

    André Platzer

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  1. André Platzer
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Sergei N. Artemov Anil Nerode

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Platzer, A. (2007). A Temporal Dynamic Logic for Verifying Hybrid System Invariants . In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_32

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  • DOI: https://doi.org/10.1007/978-3-540-72734-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72732-3

  • Online ISBN: 978-3-540-72734-7

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