中文摘要：

对于确定型有穷状态自动机（DFA）,通过定义状态集上的等价关系≈Q,借助于等价关系,可以在平方时间内构造出接受相同语言的极小化自动机.本文在DFA之间引入同态关系,证明了同态压缩下DFA接受相同语言.

英文摘要：

By defining equivalent relationship on status sets,it was proved that a new DFA（Deterministic Finite Automaton） can be constructed which accepts the same language accepted by original DFA in square time.In this paper,we defined a homomorphism relationship,and proved that the new homomorphism compression DFA acceptes the same language accepted by original DFA.