Synchronizing word
In the theory of deterministic finite automata (DFA), a synchronizing word which sends any state of an automaton to one and the same state.
The problem of estimating the length of synchronizing words has a long history and was posed independently by several authors, but it is commonly known as the Černy conjecture. In 1964 Jan Černy conjectured that (n-1)2 is the upper bound for the length of the shortest synchronizing word for any n-state complete DFA.