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 0,3 (truth table 0x16686881, canonical 0x16686881)

A minimal Boolean formula using AND, OR, and XOR requires 12 operators. One such formula is:

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

A minimal Boolean formula using AND and OR requires 26 operators. One such formula is:

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