Bdd-Based Boolean Functional Synthesis

Boolean functional synthesis is the process of automatically obtaining a constructive formalization from a declarative relation that is given as a Boolean formula. Recently, a framework was proposed for Boolean functional synthesis that is based on Craig Interpolation and in which Boolean functions are represented as And-Inverter Graphs (AIGs). In this work we adapt this framework to the setting of Binary Decision Diagrams (BDDs), a standard data structure for representation of Boolean functions. Our motivation in studying BDDs is their common usage in temporal synthesis, a fundamental technique for constructing control software/hardware from temporal specifications, in which Boolean synthesis is a basic step. Rather than using Craig Interpolation, our method relies on a technique called Self-Substitution, which can be easily implemented by using existing BDD operations. We also show that this yields a novel way to perform quantifier elimination for BDDs. In addition, we look at certain BDD structures called input-first, and propose a technique called TrimSubstitute, tailored specifically for such structures. Experiments on scalable benchmarks show that both Self-Substitution and TrimSubstitute scale well for benchmarks with good variable orders and significantly outperform current Boolean-synthesis techniques.