Abstract
An automaton is synchronizing if there exists a word driving it into a definite state regardless of the starting state. For an n-state automaton the set of synchronizing words is a regular language that can be accepted by an automaton having 2n−n states. Here, we study automata over two input letters and circular automata with n states having the property that the minimal automata for their sets of synchronizing words have 2n−n states, i.e., the minimal automata are maximal possible. We give a sufficient condition for this property that links it to completely reachable automata, non-trivial automaton congruences and the notion of uniform minimality. We apply our result to the family Kn of automata that was previously only conjectured to have this property.
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