Boolf prop/3-ary/Zhegalkin deviation
< Boolf prop < 3-ary

The values are Zhegalkin indices. The corresponding BF are those whose Zhegalkin linear is the contradiction.

Every Z.d. can be denoted by the prefect of the twin.
The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.
But this is an exception for arity 3.

Z.d. and t.p. can be merged into Z.d. faction and t.p. signed weight.
The image shows signed weight ¬2, the union of twin prefects ¬3, ¬5, ¬6.

The twin prefect is the signed consul.

Ж 232 (SAND)
This is the XOR of Z.d. whose corresponding t.p. are n and ¬n.


The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.
But this is an exception for arity 3.

The image shows signed weight ¬2, the union of twin prefects ¬3, ¬5, ¬6.


This is the XOR of Z.d. whose corresponding t.p. are n and ¬n.
Number of blocks: 16 Integer partition: 16⋅16
| # | Zhegalkin deviation |
twin prefect |
block |
|---|---|---|---|
| 16 | 0 0 Ж 0 |
0, 0 0 |
[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]![]() |
| 16 | 232 104 Ж 232 |
0, 1 ¬0 |
[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]![]() |
| 16 | 168 168 Ж 168 |
1, 0 1 |
[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]![]() |
| 16 | 64 192 Ж 64 |
1, 1 ¬1 |
[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]![]() |
| 16 | 200 200 Ж 200 |
2, 0 2 |
[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]![]() |
| 16 | 32 160 Ж 32 |
2, 1 ¬2 |
[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]![]() |
| 16 | 96 96 Ж 96 |
3, 0 3 |
[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]![]() |
| 16 | 136 8 Ж 136 |
3, 1 ¬3 |
[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]![]() |
| 16 | 224 224 Ж 224 |
4, 0 4 |
[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]![]() |
| 16 | 8 136 Ж 8 |
4, 1 ¬4 |
[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]![]() |
| 16 | 72 72 Ж 72 |
5, 0 5 |
[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]![]() |
| 16 | 160 32 Ж 160 |
5, 1 ¬5 |
[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]![]() |
| 16 | 40 40 Ж 40 |
6, 0 6 |
[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]![]() |
| 16 | 192 64 Ж 192 |
6, 1 ¬6 |
[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]![]() |
| 16 | 128 128 Ж 128 |
7, 0 7 |
[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]![]() |
| 16 | 104 232 Ж 104 |
7, 1 ¬7 |
[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]![]() |















