Properties of Boolean functions/soft/permutation

Studies of Boolean functions

Properties of Boolean functions
hard	soft
binary	binary
integer	integer
permutation	permutation

Soft properties depend on the arity of the BF.
Permutations assign each BF to a unique BF.

twin

The Zhegalkin twin of a BF is its Zhegalkin index interpreted as a truth table of length 2^arity.

partner and friend

The partner/friend of a BF differs from its truth table in the least/most significant bit.
E.g. 0110 has the partner 1110 and the friend 0111.

half-complement

The half-complement of a BF is its XOR with x_arity−1.   See e.g. the half-complements of $A\land B$:

• arity 3:       $(A\land B)\oplus C$       0001 0001 XOR 0000 1111 = 0001 1110
• arity 4:       $(A\land B)\oplus D$       0001 0001 0001 0001 XOR 0000 0000 1111 1111 = 0001 0001 1110 1110