Bi-decomposing large Boolean functions via interpolation and satisfiability solving

Boolean function bi-decomposition is a fundamental operation in logic synthesis. A function ƒ(X) is bi-decomposable under a variable partition X
A
, X
B
, X
C
on X if it can be written as h(ƒ
A
(X
A
,X
C
), ƒ
B
(X
B
,X
C
)) for some functions h, ƒ
A
, and ƒ
B
. The quality of a bi-decomposition is mainly determined by its variable partition. A preferred decomposition is disjoint, i.e. X
C
= ø, and balanced, i.e. |X
A
| ≈ |X
B
|. Finding such a good decomposition reduces communication and circuit complexity, and yields simple physical design solutions. Prior BDD-based methods may not be scalable to decompose large functions due to the memory explosion problem. Also as decomposability is checked under a fixed variable partition, searching a good or feasible partition may run through costly enumeration that requires separate and independent decomposability checkings. This paper proposes a solution to these difficulties using interpolation and incremental SAT solving. Preliminary experimental results show that the capacity of bi-decomposition can be scaled up substantially to handle large designs.