Nicolas Markey

Résumé

Timed automata are governed by an idealized semantics that assumes a perfectly precise behavior of the clocks. The traditional semantics is not robust because the slightest perturbation in the timing of actions may lead to completely different behaviors of the automaton. Following several recent works, we consider a relaxation of this semantics, in which guards on transitions are widened by Δ>0 and clocks can drift by ε>0. The relaxed semantics encompasses the imprecisions that are inevitably present in an implementation of a timed automaton, due to the finite precision of digital clocks.

We solve the safety verification problem for this robust semantics: given a timed automaton and a set of bad states, our algorithm decides if there exist positive values for the parameters Δ and ε such that the timed automaton never enters the bad states under the relaxed semantics.

@article{fmsd33(1-3)-DDMR,
  author =              {De{~}Wulf, Martin and Doyen, Laurent and Markey,
                         Nicolas and Raskin, Jean-Fran{\c c}ois},
  title =               {Robust Safety of Timed Automata},
  publisher =           {Springer-Verlag},
  journal =             {Formal Methods in System Design},
  volume =              {33},
  number =              {1-3},
  pages =               {45-84},
  year =                {2008},
  month =               dec,
  doi =                 {10.1007/s10703-008-0056-7},
  abstract =            {Timed automata are governed by an idealized
                         semantics that assumes a perfectly precise behavior
                         of the clocks. The traditional semantics is not
                         robust because the slightest perturbation in the
                         timing of actions may lead to completely different
                         behaviors of the automaton. Following several recent
                         works, we consider a relaxation of this semantics,
                         in which guards on transitions are widened
                         by~\(\Delta>0\) and clocks can drift
                         by~\(\epsilon>0\). The relaxed semantics encompasses
                         the imprecisions that are inevitably present in an
                         implementation of a timed automaton, due to the
                         finite precision of digital clocks.\par We solve the
                         safety verification problem for this robust
                         semantics: given a timed automaton and a set of bad
                         states, our algorithm decides if there exist
                         positive values for the parameters~\(\Delta\)
                         and~\(\epsilon\) such that the timed automaton never
                         enters the bad states under the relaxed semantics.},
}