On the Bound of the Synchronization Delay of a Local Automaton

Abstract The synchronization delay of an N-state local automaton is known to be O(N2). It has been conjectured by Kim et al. (1991) that, for deterministic local automata, it is O(N1.5) on a two-letter alphabet and no less than O(N2) in the general case. We prove that this conjecture is false and that the synchronization delay is Ω(N 2 ) in all cases.