The Cerný conjecture for automata respecting intervals of a directed graph
Mariusz Grech, Andrzej Kisielewicz · Discrete Mathematics & Theoretical Computer Science · 2013
Automata, Logic and Semantics 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.