行单项矩阵和Černy猜想，简短证明
Row monomial matrices and Černy conjecture, short proof
摘要：
我们的主要对象是一类具有一些非标准求和和常用乘法运算的行单项矩阵（每行有一个单位，其余为零）。这些矩阵生成关于上述操作的空间。在确定性有限自动机（DFA）的底层图的边缘上的字母字w称为同步，如果w将自动机的所有状态发送到唯一状态J. Černy在1964年发现了具有长度为（n-1）（n-1）的最小同步字的n状态完全DFA序列。这个假设，今天被称为Černy猜想，声称（n-1）（n-1）也是完全DFA中这样一个词的长度的精确上限。这个假说是斯塔克在1966年提出的。这个问题已经激发了大量和不断增长的调查和归纳。给出了Černy-Starke猜想的证明：确定性完全n态同步自动机的同步字长至多为（n-1）（n-1）.证明利用了空间维数与自动机底层图中边路径上单词长度之间的关系。
英文摘要：
The class of row monomial matrices (one unit and rest zeros in every row) with some non-standard operations of summation and usual multiplication is our main object. These matrices generate a space with respect to the mentioned operations. A word w of letters on edges of underlying graph of deterministic finite automaton (DFA) is called synchronizing if w sends all states of the automaton to a unique state J. Černy discovered in 1964 a sequence of n-state complete DFA possessing a minimal synchronizing word of length (n-1)(n-1). The hypothesis, well known today as the Černy conjecture, claims that (n-1)(n-1) is also precise upper bound on the length of such a word for a complete DFA. The hypothesis was formulated in 1966 by Starke. The problem has motivated great and constantly growing number of investigations and generalizations. We present the proof of the Černy-Starke conjecture: the deterministic complete n-state synchronizing automaton has synchronizing word of length at most (n-1)(n-1). The proof used connection between dimension of the space and the length of words on paths of edges in underlying graph of automaton.
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