摘要
实现DFAM=(Q,Σ,δ,q0,F)最小化算法的关键问题是如何编程求取商集Q/Rk(即状态的k阶区分).引入等价关系Sk与商集Q/Sk(状态的严格k阶区分),证明了Rk=Rk-1∩Sk,因此Q/Rk是Q/Rk-1中等价类与Q/Sk中等价类的非空交集全体.为了求取Q/Sk,引入Q的子集Hk,提出了利用集合的交、差运算可由Hk求取Q/Sk,从而仅利用集合运算便可求取Q/Rk的算法.基于上述理论分析,给出了DFA最小化算法的一个容易实现的构造性描述及示例.
A key problem of implementing the minimization algorithm of DFAM = （ Q,∑,δ,q0,F） is how to program to solve quotient set Q/Rk （i. e. k-order partition of states）. An equivalence relation Sk on Q and quotient set Q/Sk （exact k-order partition of states） are introduced, and Rk = Rk-1 N Sk is proved. The elements of Q/Rk are all nonempty intersections with each equivalence class belonging to Q/Rk-1 and each one belonging to Q/ Sk . A subset Hk of Q is introduced for solving Q/Sk using only intersection and difference operations, and therefore Q/Rk is solved using only set operations. A constructive minimization algorithm of DFA easy to be implemented is presented based on the above discussion.
出处
《湖北工业大学学报》
2006年第2期69-71,共3页
Journal of Hubei University of Technology
关键词
有限自动机
等价最小有限自动机
等价关系
商集
deterministic finite automata
minimum equivalent finite automaton
equivalence relation
quotient set
partition
作者简介
韩光辉（1956-），男，湖北武汉人，武汉商业服务学院副教授，研究方向：计算理论与人工智能．
