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The Cerný conjecture for automata respecting intervals of a directed graph

Abstract : The Cerný's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n - 1)2. We prove this conjecture for a class of automata preserving certain properties of intervals of a directed graph. Our result unifies and generalizes some earlier results obtained by other authors.
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Mariusz Grech, Andrzej Kisielewicz. The Cerný conjecture for automata respecting intervals of a directed graph. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 3 (3), pp.61--72. ⟨hal-00966381⟩

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