Revisiting Digitization, Robustness, and Decidability for Timed Automata

  • Authors:

  • Joël Ouaknine;James Worrell

  • Affiliations:

  • -;-

  • Venue:
  • LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2003

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Abstract

We consider several questions related to the use of digitization techniquesfor timed automata. These very successful techniques reducedense-time language inclusion problems to discrete time, but are applicableonly when the implementation is closed under digitization andthe specification is closed under inverse digitization. We show that,for timed automata, the former (whether the implementation is closedunder digitization) is decidable, but not the latter. We also investigatedigitization questions in connection with the robust semantics fortimed automata. The robust modelling approach introduces a timingfuzziness through the semantic removal of equality testing. Since itsintroduction half a decade ago, research into the robust semantics hassuggested that it yields roughly the same theory as the standard semantics.This paper shows that, surprisingly, this is not the case: the robustsemantics is significantly less tractable, and differs from the standardsemantics in many key respects. In particular, the robust semanticsyields an undecidable (non-regular) discrete-time theory, in stark contrastwith the standard semantics. This makes it virtually impossible toapply digitization techniques together with the robust semantics. Onthe positive side, we show that the robust languages of timed automataremain recursive.