Synchronizing Automata with Extremal Properties

  title={Synchronizing Automata with Extremal Properties},
  author={Andrzej Kisielewicz and Marek Szykula},
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length Θ(n 2), where n is the number of states of the automaton. This disproves a conjecture that every subset in a strongly connected synchronizing automaton is cn-extendable, for some constant c, and in particular, shows that the cubic upper bound on the length of the shortest reset words… CONTINUE READING
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