Bi-decomposing large Boolean functions via interpolation and satisfiability solving

Abstract

Boolean function bi-decomposition is a fundamental operation in logic synthesis. A function f(X) is bi-decomposable under a variable partition X_A, X_B, X_C on X if it can be written as h(f_A(X_A, X_C), f_B(X_B, X_C)) for some functions h, Ja, and /#. The quality of a bi-decomposition is mainly determined by its variable partition. A preferred decomposition is disjoint, i.e. X_C = Oslash, and balanced, i.e. |X_A| ap |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.