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
- 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.png) 255 1111 1111 |
.svg.png) 254 0111 1111 |
.svg.png) 127 1111 1110 |
.svg.png) 126 0111 1110 |
 |
| Zhegalkin indices |
.svg.png) 128 0000 0001 |
.svg.png) 129 1000 0001 | |||
symmetric
Symmetric BF do not depend on the order of their inputs. (They are the unique members of their factions.)
noble
Noble BF are their own Zhegalkin twins.
crested
BF is crested, iff its faction XOR is different from that of its complement. See crest.