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Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets

  • Patricia Bouyer
  • Thomas Brihaye
  • Marcin Jurdziński
  • Ranko Lazić
  • Michał Rutkowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5215)

Abstract

We introduce and study hybrid automata with strong resets. They generalize o-minimal hybrid automata, a class of hybrid automata which allows modeling of complex continuous dynamics. A number of analysis problems, such as reachability testing and controller synthesis, are decidable for classes of o-minimal hybrid automata. We generalize existing decidability results for controller synthesis on hybrid automata and we establish new ones by proving that average-price and reachability-price games on hybrid systems with strong resets are decidable, provided that the structure on which the hybrid automaton is defined has a decidable first-order theory. Our proof techniques include a novel characterization of values in games on hybrid systems by optimality equations, and a definition of a new finitary equivalence relation on the states of a hybrid system which enables a reduction of games on hybrid systems to games on finite graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Thomas Brihaye
    • 2
  • Marcin Jurdziński
    • 3
  • Ranko Lazić
    • 3
  • Michał Rutkowski
    • 3
  1. 1.LSV, CNRS & ENS de CachanFrance
  2. 2.Institut de MathématiquesUniversity of Mons-HainautBelgium
  3. 3.Department of Computer ScienceUniversity of WarwickUK

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