My current approach to investigating reversible quantum gates requires the solution of Boolean functional equations. For example,
$$f(x,y,z) = f(x,y \oplus f(x,y,z), z \oplus f(x, y, z)),$$
where $f\colon B^3 \to B$, $B = \{0, 1\}$, and $\oplus$ is xor.
I have solved this one, and a number of similar types, but I do not know of an approach to solving similar equations with a higher number of variables. Is there a general algebraic approach to the solution of Boolean functional equations of this, or similar, types?