Properties of Boolean functions/soft/permutation

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

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

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.

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

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