  A word w is called synchronizing (recurrent, reset, directed) word of a
deterministic finite automaton (DFA) if w sends all states of the automaton on
a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA
with shortest synchronizing word of length (n-1)^2. He had conjectured that it
is an upper bound for the length of the shortest synchronizing word for any
$n$-state complete DFA.
  The examples of DFA with shortest synchronizing word of length (n-1)^2 are
relatively rare. To the Cerny sequence were added in all examples of Cerny,
Piricka and Rosenauerova (1971), of Kari (2001) and of Roman (2004).
  By help of a program based on some effective algorithms, a wide class of
automata of size less than 11 was checked. The order of the algorithm finding
synchronizing word is quadratic for overwhelming majority of known to date
automata. Some new examples of n-state DFA with minimal synchronizing word of
length (n-1)^2 were discovered. The program recognized some remarkable trends
concerning the length of the minimal synchronizing word.
http://www.cs.biu.ac.il/~trakht/Testas.html
