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Dynamically-Driven Timed Automaton Abstractions for Proving Liveness of Continuous Systems

  • Rebekah Carter
  • Eva M. Navarro-López
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7595)

Abstract

We look at the problem of proving inevitability of continuous dynamical systems. An inevitability property says that a region of the state space will eventually be reached: this is a type of liveness property from the computer science viewpoint, and is related to attractivity of sets in dynamical systems. We consider a method of Maler and Batt to make an abstraction of a continuous dynamical system to a timed automaton, and show that a potentially infinite number of splits will be made if the splitting of the state space is made arbitrarily. To solve this problem, we define a method which creates a finite-sized timed automaton abstraction for a class of linear dynamical systems, and show that this timed abstraction proves inevitability.

Keywords

Continuous-time systems Abstraction Automated verification Liveness properties Timed automata 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rebekah Carter
    • 1
  • Eva M. Navarro-López
    • 1
  1. 1.School of Computer ScienceThe University of ManchesterUK

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