Properties of Boolean functions/soft/binary
| Properties of Boolean functions | |
|---|---|
| hard | soft |
| binary | binary |
| integer | integer |
| permutation | permutation |
Soft properties depend on the arity of the BF.
Binary properties have the values true or false, so they partition all BF into a subset and the rest.
number of true places in the truth table of length 2arity (hard weight is a fraction)
related to parity
[edit | edit source]- BF is sharp/blunt iff weight of the truth table is odd/even. This is an important property of families.
- rude = odd XOR sharp
- rough = odious XOR sharp
- acute = ugly XOR sharp The opposite is obtuse.
| images for arity 3 | |||||
|---|---|---|---|---|---|
| sharp | rude | rough | acute | ||
| truth tables |
.svg) 255 1111 1111 |
.svg) 254 0111 1111 |
.svg) 127 1111 1110 |
.svg) 126 0111 1110 |
 |
| Zhegalkin indices |
.svg) 128 0000 0001 |
.svg) 129 1000 0001 | |||
symmetric
[edit | edit source]Symmetric BF do not depend on the order of their inputs. (They are the unique members of their factions.)
noble
[edit | edit source]Noble BF are their own Zhegalkin twins.
crested
[edit | edit source]BF is crested, iff its faction XOR is different from that of its complement. See crest.