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Robust Undecidability of Timed and Hybrid Systems

  • Thomas A. Henzinger
  • Jean-François Raskin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1790)

Abstract

The algorithmic approach to the analysis of timed and hybrid systems is fundamentally limited by undecidability, of universality in the timed case (where all continuous variables are clocks), and of emptiness in the rectangular case (which includes drifting clocks). Traditional proofs of undecidability encode a single Turing computation by a single timed trajectory. These proofs have nurtured the hope that the introduction of “fuzziness” into timed and hybrid models (in the sense that a system cannot distinguish between trajectories that are sufficiently similar) may lead to decidability. We show that this is not the case, by sharpening both fundamental undecidability results. Besides the obvious blow our results deal to the algorithmic method, they also prove that the standard model of timed and hybrid systems, while not “robust” in its definition of trajectory acceptance (which is affected by tiny perturbations in the timing of events), is quite robust in its mathematical properties: the undecidability barriers are not affected by reasonable perturbations of the model.

Keywords

Hybrid System Positive Real Hybrid Automaton Time Automaton Open Slot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Jean-François Raskin
    • 1
    • 2
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyUSA
  2. 2.Département d’Informatique, Faculté des SciencesUniversité Libre de BruxellesBelgium

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