It was conjectured by Černý in 1964 that a synchronizing DFA on n states always has a shortest synchronizing word of length at most ${(n-1)}^2$, and he gave a sequence of DFAs reaching this bound.

In this paper, we investigate the role of the alphabet size. For each possible alphabet size, we count DFAs on $n\le 6$ states which synchronize in ${(n-1)}^2-e$ steps, for all $e<2\lceil n/2\rceil$. Furthermore, we give constructions of automata with any number of states, and 3, 4, or 5 symbols, which synchronize slowly, namely in $n^2-3n+O(1)$ steps.

In addition, our results prove Černý's conjecture for $n\le 6$. Our computations lead to 31 DFAs on 3, 4, 5 or 6 states, which synchronize in ${(n-1)}^2$ steps. Of these DFA's, 19 are new. The remaining 12, which were already known, are exactly the minimal ones.

The 19 new DFAs are extensions of automata which were already known. But for $n>3$, we prove that the Černý automaton on n states does not admit non-trivial extensions with the same smallest synchronizing word length ${(n-1)}^2$.

Černý 在 1964 年推测，n个状态上的同步 DFA总是有一个最短的同步字长度至多${(n-1)}^2$，他给出了达到这个界限的一系列 DFA。

在本文中，我们研究了字母大小的作用。对于每个可能的字母大小，我们计算 DFA$n\le 6$ 同步的状态 ${(n-1)}^2-\mathrm{电子}$ 步骤，对于所有 $\mathrm{电子}<2\lceil n/2\rceil$. 此外，我们给出了具有任意数量状态和 3、4 或 5 个符号的自动机的构造，这些符号同步缓慢，即在$n^2-3n+哦(1)$ 脚步。

此外，我们的结果证明了 Černý 猜想 $n\le 6$. 我们的计算在 3、4、5 或 6 个状态上产生了 31 个 DFA，它们在${(n-1)}^2$脚步。在这些 DFA 中，有 19 个是新的。剩下的 12 个，已知的，正是最小的。

19 个新的 DFA 是已知的自动机的扩展。但对于$n>3$，我们证明了n个状态上的 Černý 自动机不接受具有相同最小同步字长的非平凡扩展${(n-1)}^2$.