Properties of Boolean functions/hard/permutation
| Studies of Boolean functions |
| Properties of Boolean functions | |
|---|---|
| hard | soft |
| binary | binary |
| integer | integer |
| permutation | permutation |
Hard properties can be assigned to a BF, without referencing its arity.
Permutations assign each BF to a unique BF.
complement
[edit | edit source]all places of the truth table negated, e.g. 0001 and 1110 (LSB of the Zhegalkin index negated)
The complement of a set of BF is the set of complements. (Families and clans can be self-complementary. Factions can not.)
reverse
[edit | edit source]truth table reversed, e.g. 0001 and 1000
dual
[edit | edit source]complement of the reverse, e.g. 0001 and 0111