java实现dfa化简

DFA（确定有限状态自动机）的化简是将一个复杂的DFA转化为一个更简单的DFA，其实现过程主要有以下几个步骤：

1. 消除不可达状态：从起始状态出发，通过转移函数能够到达的状态称为可达状态，不能到达的状态称为不可达状态。将所有不可达状态删除。

2. 合并等价状态：将可以相互到达的状态合并为一个状态，使得新的DFA中状态数最少。通过等价关系划分算法，对状态进行分组，分组后的状态就是等价状态。

3. 构造化简后的DFA：根据等价状态分组的结果，构造化简后的DFA。

下面是Java实现DFA化简的示例代码：

import java.util.*;

public class DFAMinimization {

    public static void main(String[] args) {
        int[][] transition = {{1,2},{2,3},{3,4},{4,5},{5,6},{6,7},{7,8},{8,9},{9,10},{10,11},{11,12},{12,13},{13,14},{14,15},{15,16},{16,17},{17,18},{18,19},{19,20},{20,21},{21,22},{22,23},{23,24},{24,25},{25,26},{26,27},{27,28},{28,29},{29,30},{30,31},{31,32},{32,33},{33,34},{34,35},{35,36},{36,37},{37,38},{38,39},{39,40},{40,41},{41,42},{42,43},{43,44},{44,45},{45,46},{46,47},{47,48},{48,49},{49,50},{50,51},{51,52},{52,53},{53,54},{54,55},{55,56},{56,57},{57,58},{58,59},{59,60},{60,61},{61,62},{62,63},{63,64},{64,65},{65,66},{66,67},{67,68},{68,69},{69,70},{70,71},{71,72},{72,73},{73,74},{74,75},{75,76},{76,77},{77,78},{78,79},{79,80},{80,81},{81,82},{82,83},{83,84},{84,85},{85,86},{86,87},{87,88},{88,89},{89,90},{90,91},{91,92},{92,93},{93,94},{94,95},{95,96},{96,97},{97,98},{98,99},{99,100},{100,100}};
        int[] finalStates = {100};
        DFAMinimization dfaMinimization = new DFAMinimization();
        dfaMinimization.minimize(transition, finalStates);
    }

    public void minimize(int[][] transition, int[] finalStates) {
        int n = transition.length;
        int[][] partition = new int[2][n];
        boolean[][] marked = new boolean[n][n];
        for (int i = 0; i < n; i++) {
            partition[0][i] = i;
            for (int j = 0; j < n; j++) {
                marked[i][j] = finalStates[i] != finalStates[j];
            }
        }
        boolean changed = true;
        while (changed) {
            changed = false;
            for (int i = 0; i < n; i++) {
                for (int j = i+1; j < n; j++) {
                    if (!marked[i][j]) {
                        for (int k = 0; k < 2; k++) {
                            int pi = partition[k][i];
                            int pj = partition[k][j];
                            if (pi != pj) {
                                partition[k][i] = Math.min(pi, pj);
                                partition[k][j] = Math.min(pi, pj);
                                changed = true;
                            }
                        }
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    marked[i][j] = false;
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = i+1; j < n; j++) {
                    if (!marked[i][j]) {
                        for (int x = 0; x < 2; x++) {
                            for (int y = 0; y < 2; y++) {
                                int pi = partition[x][i];
                                int pj = partition[y][j];
                                if (!marked[pi][pj]) {
                                    for (int k = 0; k < n; k++) {
                                        int pk = transition[k][i];
                                        int pl = transition[k][j];
                                        if (marked[pk][pl]) {
                                            marked[pi][pj] = true;
                                            changed = true;
                                            break;
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        int[] map = new int[n];
        Arrays.fill(map, -1);
        int count = 0;
        for (int i = 0; i < n; i++) {
            if (map[i] == -1) {
                map[i] = count++;
                for (int j = i+1; j < n; j++) {
                    if (!marked[i][j]) {
                        map[j] = map[i];
                    }
                }
            }
        }
        int[][] newTransition = new int[n][];
        int[] newFinalStates = new int[count];
        int newCount = 0;
        for (int i = 0; i < count; i++) {
            boolean isFinal = false;
            for (int j = 0; j < n; j++) {
                if (map[j] == i) {
                    if (finalStates[j] != -1) {
                        isFinal = true;
                    }
                    if (newTransition[i] == null) {
                        newTransition[i] = new int[n];
                    }
                    for (int k = 0; k < n; k++) {
                        newTransition[i][k] = map[transition[k][j]];
                    }
                }
            }
            if (isFinal) {
                newFinalStates[newCount++] = i;
            }
        }
        newFinalStates = Arrays.copyOf(newFinalStates, newCount);
        System.out.println(Arrays.deepToString(newTransition));
        System.out.println(Arrays.toString(newFinalStates));
    }
}

以上代码实现了DFA的化简，其中transition数组表示状态转移矩阵，finalStates数组表示终止状态集合。具体实现过程中，使用等价关系划分算法对状态进行分组，最终得到化简后的DFA状态转移矩阵和终止状态集合。