Authors: Mariusz Grech ¹; Andrzej Kisielewicz ¹

• 1 Mathematical Institute [Wroclaw]

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.