### The Černý conjecture for automata respecting intervals of a directed graph

*Mariusz Grech, Andrzej Kisielewicz*

#### Abstract

The Černý'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.Full Text: PDF PostScript