Synthesis with Explicit Dependencies

Abstract: Quantified Boolean Formulas (QBF) extend propositional logic with quantification $\forall, \exists$. In QBF, an existentially quantified variable is allowed to depend on all universally quantified variables in its scope. Dependency Quantified Boolean Formulas (DQBF) restrict the dependencies of existentially quantified variables. In DQBF, existentially quantified variables have explicit dependencies on a subset of universally quantified variables called Henkin dependencies. Given a Boolean specification between the set of inputs and outputs, the problem of Henkin synthesis is to synthesize each output variable as a function of its Henkin dependencies such that the specification is met. Henkin synthesis has wide-ranging applications, including verification of partial circuits, controller synthesis, and circuit realizability. This work proposes a data-driven approach for Henkin synthesis called Manthan3. On an extensive evaluation of over 563 instances arising from past DQBF solving competitions, we demonstrate that Manthan3 is competitive with state-of-the-art tools. Furthermore, Manthan3 could synthesize Henkin functions for 26 benchmarks for which none of the state-of-the-art techniques could synthesize.