Synchronization of finite automata

Abstract

A survey of the state-of-the-art of the theory of synchronizing automata is given in its part concerned with the case of complete deterministic automata. Algorithmic and complexity-theoretic aspects are considered, the existing results related to Černý's conjecture and methods for their derivation are presented. Bibliography: 193 titles.

Binary Completely Reachable Automata

“…Any such w is said to be a reset word for the DFA. We refer the reader to the chapter [10] of the 'Handbook of Automata Theory' or to the second-named author's survey [13] for an introduction to the rich theory of synchronizing automata. Here we only say that much research in this area groups around the famous Černý conjecture that every synchronizing automaton with n states admits a reset word of length at most (n − 1) 2 .…”