Nicolas Markey

Abstract

Timed automata follow a mathematical semantics, which assumes perfect precision and synchrony of clocks. Since this hypothesis does not hold in digital systems, properties proven formally on a timed automaton may be lost at implementation. In order to ensure implementability, several approaches have been considered, corresponding to different hypotheses on the implementation platform. We address two of these: a timed automaton is samplable if its semantics is preserved under a discretization of time; it is robust if its semantics is preserved when all timing constraints are relaxed by some small positive parameter. We propose a construction which makes timed automata implementable in the above sense: From any timed automaton A, we build a timed automaton A' that exhibits the same behaviour as A, and moreover is both robust and samplable by construction.

@inproceedings{concur2011-BLMST,
  author =              {Bouyer, Patricia and Larsen, Kim Guldstrand and
                         Markey, Nicolas and Sankur, Ocan and Thrane, Claus},
  title =               {Timed automata can always be made implementable},
  editor =              {Katoen, Joost-Pieter and K{\"o}nig, Barbara},
  booktitle =           {{P}roceedings of the 22nd {I}nternational
                         {C}onference on {C}oncurrency {T}heory
                         ({CONCUR}'11)},
  acronym =             {{CONCUR}'11},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {6901},
  pages =               {76-91},
  year =                {2011},
  month =               sep,
  doi =                 {10.1007/978-3-642-23217-6_6},
  abstract =            {Timed automata follow a mathematical semantics,
                         which assumes perfect precision and synchrony of
                         clocks. Since this hypothesis does not hold in
                         digital systems, properties proven formally on a
                         timed automaton may be lost at implementation. In
                         order to ensure implementability, several approaches
                         have been considered, corresponding to different
                         hypotheses on the implementation platform. We
                         address two of these: a~timed automaton is samplable
                         if its semantics is preserved under a discretization
                         of time; it is robust if its semantics is preserved
                         when all timing constraints are relaxed by some
                         small positive parameter. We propose a construction
                         which makes timed automata implementable in the
                         above sense: From any timed
                         automaton~\(\mathcal{A}\), we build a timed
                         automaton~\(\mathcal{A}'\) that exhibits the same
                         behaviour as~\(\mathcal{A}\), and moreover is both
                         robust and samplable by construction.},
}