dfa最简化代码c++

以下是一个用C语言实现DFA最小化的示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

#define STATES 6
#define SYMBOLS 2

int transition[STATES][SYMBOLS] = {
    {1, 2},
    {1, 3},
    {4, 2},
    {1, 5},
    {4, 2},
    {4, 5}
};

bool is_final[STATES] = {false, true, false, true, true, true};

int find_group(int state, int groups[][STATES]) {
    for (int i = 0; i < STATES; i++) {
        for (int j = 0; j < STATES; j++) {
            if (groups[i][j] == state) {
                return i;
            }
        }
    }
    return -1;
}

bool is_same_group(int state1, int state2, int groups[][STATES]) {
    int group1 = find_group(state1, groups);
    int group2 = find_group(state2, groups);
    return group1 == group2;
}

void print_groups(int groups[][STATES], int num_groups) {
    for (int i = 0; i < num_groups; i++) {
        printf("Group %d: ", i+1);
        for (int j = 0; j < STATES; j++) {
            if (groups[i][j] != -1) {
                printf("%d ", groups[i][j]);
            }
        }
        printf("\n");
    }
}

void minimize_dfa() {
    int groups[STATES][STATES] = {{0}};
    int num_groups = 0;
    for (int i = 0; i < STATES; i++) {
        groups[0][i] = i;
    }
    num_groups++;

    // Divide states into final and non-final groups
    int final_group[STATES], non_final_group[STATES];
    int num_final = 0, num_non_final = 0;
    for (int i = 0; i < STATES; i++) {
        if (is_final[i]) {
            final_group[num_final++] = i;
        } else {
            non_final_group[num_non_final++] = i;
        }
    }
    groups[1][0] = final_group[0];
    groups[2][0] = non_final_group[0];
    num_groups = 3;

    // Continue dividing the groups until no more changes occur
    bool changed = true;
    while (changed) {
        changed = false;
        int new_groups[STATES][STATES] = {{-1}};
        int new_num_groups = 0;
        for (int i = 0; i < num_groups; i++) {
            for (int j = 0; j < STATES; j++) {
                if (groups[i][j] == -1) {
                    break;
                }
                int group_index = -1;
                for (int k = 0; k < new_num_groups; k++) {
                    if (is_same_group(groups[i][j], new_groups[k][0], groups)) {
                        group_index = k;
                        break;
                    }
                }
                if (group_index == -1) {
                    group_index = new_num_groups++;
                    new_groups[group_index][0] = groups[i][j];
                } else {
                    changed = true;
                }
                for (int k = 0; k < SYMBOLS; k++) {
                    int next_state = transition[groups[i][j]][k];
                    if (next_state == -1) {
                        continue;
                    }
                    if (!is_same_group(next_state, new_groups[group_index][0], groups)) {
                        new_groups[group_index][new_groups[group_index][0] == -1 ? 0 : ++new_groups[group_index][0]] = next_state;
                        changed = true;
                    }
                }
            }
        }
        for (int i = 0; i < new_num_groups; i++) {
            for (int j = 0; j < STATES; j++) {
                groups[i][j] = new_groups[i][j];
            }
        }
        num_groups = new_num_groups;
    }

    // Print the final minimized DFA
    printf("Minimized DFA:\n");
    for (int i = 0; i < num_groups; i++) {
        int state = groups[i][0];
        printf("State %d: ", i+1);
        for (int j = 0; j < SYMBOLS; j++) {
            int next_state = transition[state][j];
            if (next_state == -1) {
                printf("- ");
                continue;
            }
            printf("%d ", find_group(next_state, groups) + 1);
        }
        printf("%s\n", is_final[state] ? "(final)" : "");
    }
    printf("\n");

    // Print the groups
    printf("Groups:\n");
    print_groups(groups, num_groups);
}

int main() {
    minimize_dfa();
    return 0;
}

该代码的主要思路是将DFA状态分组，然后根据状态转移表来判断哪些状态应该被分为同一组。在每次迭代中，将当前分组中的状态按照其下一个状态所在的组进行重新分组，直到没有状态发生更改为止。最后，将每个组作为一个新的状态，并生成最小化的DFA状态转移表。