Interesting Functions

Hardest n-input for (AND, OR, XOR)
(1) 1
(2) x+y = 1
(3) x+y+z = 1
(4) x+y+z+w = 1
(5) x+y+z+w+v in 0,3

Hardest n-input for (AND, OR)
(1) 1
(2) x^y
(3) x^y^z
(4) x^y^z^w
(5) x+y+z+w+v in 0,1,3,
x+y+z+w+v in 0,1,3 || x&y&z&w&!v,
x+y+z+w+v in 1,3 || x&y&z&w&!v

Boolean Oracle

This web server computes a minimal Boolean formula for a given function, using the operator sets (AND, OR, XOR) and (AND, OR).

Query: x+y+z+w+v in 0,1,3 (truth table 0x16696997, canonical 0x16696997)

A minimal Boolean formula using AND, OR, and XOR requires 10 operators. One such formula is:

¬w ^ v ^ ¬x ^ ((y ^ z) | ((¬x ^ w) & (¬y ^ v) & (¬z ^ x)))

A minimal Boolean formula using AND and OR requires 28 operators. One such formula is:

((y | ¬z) & (¬y | z) & (w | ((¬v | ¬x) & (v | x))) & (¬w | (¬v & ¬x) | (v & ¬z & x))) | ((¬y | ¬z) & (¬x | ((¬w | ¬v) & (w | v))) & ((¬w & ¬v) | ((y | z) & (x | (w & v)))))