Решение.
Минимизируем данную систему ДНФ методом Квайна-МакКласки. Получаем следующую последовательность пар матриц.
|
Х1 |
Х2 |
Х3 |
Х4 |
|
f1 |
f2 |
f3 |
|
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
|
0 |
0 |
0 |
1 |
2* |
1 |
1 |
0 |
|
1 |
1 |
0 |
1 |
3 |
0 |
1 |
1 |
|
0 |
0 |
0 |
0 |
4* |
0 |
1 |
0 |
|
1 |
0 |
0 |
0 |
5 |
0 |
1 |
1 |
|
1 |
0 |
0 |
1 |
6* |
1 |
1 |
0 |
|
0 |
1 |
0 |
0 |
7* |
0 |
0 |
1 |
|
0 |
1 |
1 |
0 |
8 |
1 |
0 |
0 |
|
0 |
1 |
0 |
1 |
9* |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
10* |
0 |
1 |
0 |
|
Х1 |
Х2 |
Х3 |
Х4 |
|
f1 |
f2 |
f3 |
|
0 |
0 |
0 |
- |
1* |
0 |
1 |
0 |
|
- |
0 |
0 |
1 |
2 |
1 |
1 |
0 |
|
0 |
- |
0 |
1 |
3 |
0 |
0 |
1 |
|
1 |
- |
0 |
1 |
4 |
0 |
1 |
0 |
|
- |
1 |
0 |
1 |
5 |
0 |
0 |
1 |
|
- |
0 |
0 |
0 |
6* |
0 |
1 |
0 |
|
0 |
0 |
- |
0 |
7 |
0 |
1 |
0 |
|
1 |
0 |
0 |
- |
8* |
0 |
1 |
0 |
|
0 |
1 |
0 |
- |
9 |
0 |
0 |
1 |
|
Х1 |
Х2 |
Х3 |
Х4 |
|
f1 |
f2 |
f3 |
|
- |
0 |
0 |
- |
|
0 |
1 |
0 |
|
- |
0 |
0 |
1 |
|
0 |
1 |
0 |
Получили сокращенную систему ДНФ, которая содержит строки, не отмеченные знаком «*»
|
Х1 |
Х2 |
Х3 |
Х4 |
|
f1 |
f2 |
f3 |
|
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
2 |
0 |
1 |
1 |
|
1 |
0 |
0 |
0 |
3 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
4 |
1 |
0 |
0 |
|
- |
0 |
0 |
1 |
5 |
1 |
1 |
0 |
|
0 |
- |
0 |
1 |
6 |
0 |
0 |
1 |
|
1 |
- |
0 |
1 |
7 |
0 |
1 |
0 |
|
- |
1 |
0 |
1 |
8 |
0 |
0 |
1 |
|
0 |
0 |
- |
0 |
9 |
0 |
1 |
0 |
|
0 |
1 |
0 |
- |
10 |
0 |
0 |
1 |
|
- |
0 |
0 |
- |
11 |
0 |
1 |
0 |
|
- |
0 |
0 |
1 |
12 |
0 |
1 |
0 |
Теперь проведем второй этап минимизации, который сводится к задаче покрытия.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
|
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
|
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
Кратчайшее строчное покрытие приведенной матрицы соответствует кратчайшей системе ДНФ, представляемой следующими матрицами:
|
Х1 |
Х2 |
Х3 |
Х4 |
|
f1 |
f2 |
f3 |
|
1 |
1 |
1 |
0 |
|
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
0 |
0 |
|
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
|
- |
0 |
0 |
1 |
|
1 |
1 |
0 |
|
0 |
0 |
- |
0 |
|
0 |
1 |
0 |
|
0 |
1 |
0 |
- |
|
0 |
0 |
1 |