Continuous Relaxation of Logic Gates

Mar 7, 2025

Differentiable Logic Cellular Automata https://google-research.github.io/self-organising-systems/difflogic-ca/

Index	Operation	Continuous relaxation
0	FALSE	$0$
1	AND	$a b$
2	A AND (NOT B)	$a - a b$
3	A	$a$
4	(NOT A) AND B	$b - a b$
5	B	$b$
6	XOR	$a + b - 2 a b$
7	OR	$a + b - a b$
8	NOR	$1 - (a + b - a b)$
9	XNOR	$1 - (a + b - 2 a b)$
10	NOT B	$1 - b$
11	A OR (NOT B)	$1 - b + a b$
12	NOT A	$1 - a$
13	(NOT A) OR B	$1 - a + a b$
14	NAND	$1 - a b$
15	TRUE	$1$