С2. МОИ. Презентации / Булевы функции 2 (v. 1.2)
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Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
2 , 3, 4 0,1,0
f (0,0,1,0) ? f (1,0,1,0)
31
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
2, 3, 4 0,1,1
f (0, , , ) ? f (1, , , )
2 3 4 2 3 4
32
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
2 , 3, 4 0,1,1
f (0,0,1,1) ? f (1,0,1,1)
33
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
2, 3, 4 0,1,1
f (0, , , ) ? f (1, , , )
2 3 4 2 3 4
34
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
2 , 3, 4 1,1,1
f (0,1,1,1) ? f (1,1,1,1)
35
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
f (0, , , ) ? f (1, , , ).
2 3 4 2 3 4
36
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
Переменная |
x2 |
является фиктивной, |
если |
|
||||||||||||
при любом выборе булевых констант 1, 3, 4
выполняется равенство
f ( 1,0, 3, 4 ) f ( 1,1, 3, 4 ).
37
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
1, 3, 4 0,0,0
f ( ,0, , ) ? f ( ,1, , )
1 3 4 1 3 4
38
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
1, 3, 4 0,0,0
f (0,0,0,0) ? f (0,1,0,0)
39
Существенные и фиктивные переменные
x1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
x2 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
x3 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
x4 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
f |
f0 |
f1 |
f2 |
f3 |
f4 |
f5 |
f6 |
f7 |
f8 |
f9 |
f10 |
f11 |
f12 |
f13 |
f14 |
f15 |
1, 3, 4 0,0,1
f ( ,0, , ) ? f ( ,1, , )
1 3 4 1 3 4
40