A Temporal Dynamic Logic for Verifying Hybrid System Invariants

  • André Platzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4514)

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.

Keywords

dynamic logic temporal logic sequent calculus logic for hybrid systems deductive verification of embedded systems 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

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

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