So far I have imposed mainly F(x,y) = F(y,x). You could also enforce F(-x,-y) = -F(x,y), but I have not done that. The second reduction that I mention is actua

So far I have imposed mainly F(x,y) = F(y,x). You could also enforce F(-x,-y) = -F(x,y), but I have not done that. The second reduction that I mention is actually to require every F to satisfy either F(-1,y) <= F(0,y) <= F(1,y) OR F(-1, y) >= F(0,y) >= F(1,y). And no the symmetries are not that useful to implement the circuitry, but are nice to select operators that compose nicely and allow many simplifications (think De Morgan's laws)