Nicolas Markey

Résumé

The problem of synchronizing automata is concerned with the existence of a word that sends all states ofM the automaton to one and the same state. This problem has classically been studied for complete deterministic finite automata, with the existence problem being NLOGSPACE-complete.

In this paper we consider synchronizing-word problems for weighted and timed automata. We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with possibly different clock valuations or accumulated weights, as well as synchronization with a safety condition forbidding the automaton to visit states outside a safety-set during synchronization (e.g. energy constraints). For deterministic weighted automata, the synchronization problem is proven PSPACE-complete under energy constraints, and in 3-EXPSPACE under general safety constraints. For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case.

@inproceedings{fsttcs2014-DJLMS,
  author =              {Doyen, Laurent and Juhl, Line and Larsen, Kim
                         Guldstrand and Markey, Nicolas and Shirmohammadi,
                         Mahsa},
  title =               {Synchronizing words for weighted and timed automata},
  editor =              {Raman, Venkatesh and Suresh, S. P.},
  booktitle =           {{P}roceedings of the 34th {C}onference on
                         {F}oundations of {S}oftware {T}echnology and
                         {T}heoretical {C}omputer {S}cience ({FSTTCS}'14)},
  acronym =             {{FSTTCS}'14},
  publisher =           {Leibniz-Zentrum f{\"u}r Informatik},
  series =              {Leibniz International Proceedings in Informatics},
  volume =              {29},
  pages =               {121-132},
  year =                {2014},
  month =               dec,
  doi =                 {10.4230/LIPIcs.FSTTCS.2014.121},
  abstract =            {The problem of synchronizing automata is concerned
                         with the existence of a word that sends all states
                         ofM the automaton to one and the same state. This
                         problem has classically been studied for complete
                         deterministic finite automata, with the existence
                         problem being NLOGSPACE-complete.\par In this paper
                         we consider synchronizing-word problems for weighted
                         and timed automata. We consider the synchronization
                         problem in several variants and combinations of
                         these, including deterministic and non-deterministic
                         timed and weighted automata, synchronization to
                         unique location with possibly different clock
                         valuations or accumulated weights, as well as
                         synchronization with a safety condition forbidding
                         the automaton to visit states outside a safety-set
                         during synchronization (e.g. energy constraints).
                         For deterministic weighted automata, the
                         synchronization problem is proven PSPACE-complete
                         under energy constraints, and in 3-EXPSPACE under
                         general safety constraints. For timed automata the
                         synchronization problems are shown to be
                         PSPACE-complete in the deterministic case, and
                         undecidable in the non-deterministic case.},
}