Determined Based On The Equivalence Class Of Non Finite Automata Minimization Method

The theory of finite automata presents a type of calculate model. This model is very important in several application fields of computer science. The finite automata includes deterministic finite automata (DFA) and non-deterministic finite automata (NFA). We call the language that the finite automata recognizes the regular language . The minimizing of the finite automata is a very important question. The minimizing here means that we transform the finite automata on the premise of equivalence . At the same time, we must make sure that the gained automata which has been transformed has the least state nodes, but it is still equivalent to the original automata. Generally speaking, the automata which has least state nodes means that it will save the software and hardware resources and the program to achieve it will be very simple.In this paper, we do some researches on the minimizing algorithm which based on equivalence in the NFA. The paper consists of three parts being mentioned below.(1) We analyze the relation between the finite automata and regular language.The paper introduce the foundation knowledge of finite automata and thecharacter of regular language and prove the equivalence of finite automata and regular expression by using the conception of automata state transform figure.(2) We analyze the algorithm of reducing DFA by equivalence.We research the equivalence of DFA and NFA, and we import equivalence relation in the set of state of DFA and give the algorithm of equivalence class, so as to create minimum automata which is equivalent to it by this algorithm.(3) We research the algorithm of reducing NFA by equivalence.We give a new minimizing NFA algorithm with minimizing algorithm of DFA which based on equivalence class. When applying this method to automata, we get an NFA from regular expression which is always smaller than the position, partial derivative, and follow automata. The experiments have proved the algorithm .