c 语言实现dfa的化简

DFA（Deterministic Finite Automaton）的化简可以通过以下步骤来实现：

1. 对于给定的DFA，确定所有等价的状态对。如果两个状态在输入相同的字符串时产生相同的输出，则这两个状态是等价的。

2. 根据等价状态对构建一个新的状态转移表。新的状态转移表中的每个状态都对应于原始DFA中的一组等价状态。

3. 如果在新的状态转移表中存在任何未使用的状态，则将这些状态移除。这样可以减少状态的数量并简化DFA。

下面是一个用C语言实现DFA化简的示例代码：

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

#define MAX_STATES 20
#define MAX_SYMBOLS 20

int dfa[MAX_STATES][MAX_SYMBOLS];
int new_dfa[MAX_STATES][MAX_SYMBOLS];
int mark[MAX_STATES][MAX_STATES];
int new_mark[MAX_STATES][MAX_STATES];
int num_states, num_symbols;

void mark_states(int state1, int state2) {
    mark[state1][state2] = mark[state2][state1] = 1;
}

int min(int a, int b) {
    return a < b ? a : b;
}

void input_dfa() {
    int i, j;
    printf("Enter the number of states: ");
    scanf("%d", &num_states);
    printf("Enter the number of input symbols: ");
    scanf("%d", &num_symbols);
    printf("Enter the DFA table:\n");
    for (i = 0; i < num_states; i++) {
        for (j = 0; j < num_symbols; j++) {
            scanf("%d", &dfa[i][j]);
        }
    }
}

void initialize_mark() {
    int i, j;
    for (i = 0; i < num_states; i++) {
        for (j = i + 1; j < num_states; j++) {
            if ((dfa[i][0] == -1 && dfa[j][0] != -1) || (dfa[i][0] != -1 && dfa[j][0] == -1)) {
                mark_states(i, j);
            }
        }
    }
}

void mark_unmarked_states() {
    int i, j;
    for (i = 0; i < num_states; i++) {
        for (j = i + 1; j < num_states; j++) {
            if (!mark[i][j]) {
                mark_states(i, j);
                int k;
                for (k = 0; k < num_symbols; k++) {
                    int p = dfa[i][k], q = dfa[j][k];
                    if (p != q) {
                        if (mark[p][q]) {
                            mark_states(i, j);
                        } else {
                            mark_unmarked_states();
                        }
                    }
                }
            }
        }
    }
}

void create_new_dfa() {
    int i, j, cnt = 0;
    for (i = 0; i < num_states; i++) {
        for (j = i + 1; j < num_states; j++) {
            if (!mark[i][j]) {
                int k;
                for (k = 0; k < num_symbols; k++) {
                    new_dfa[i][k] = new_dfa[j][k] = -1;
                }
            }
        }
    }
    for (i = 0; i < num_states; i++) {
        int k;
        for (k = 0; k < num_symbols; k++) {
            int p = dfa[i][k], j;
            for (j = i + 1; j < num_states; j++) {
                if (!mark[i][j]) {
                    continue;
                }
                int q = dfa[j][k];
                int x = min(i, j), y = max(i, j);
                if (new_dfa[x][k] == -1) {
                    new_dfa[x][k] = new_dfa[y][k] = cnt++;
                }
            }
        }
    }
    num_states = cnt;
    memcpy(dfa, new_dfa, sizeof(new_dfa));
}

int main() {
    input_dfa();
    initialize_mark();
    mark_unmarked_states();
    create_new_dfa();
    printf("The simplified DFA table is:\n");
    int i, j;
    for (i = 0; i < num_states; i++) {
        for (j = 0; j < num_symbols; j++) {
            printf("%d ", dfa[i][j]);
        }
        printf("\n");
    }
    return 0;
}

该示例代码输入DFA表，并根据等价状态对构建新的DFA表，最后输出化简后的DFA表。