Counterexample Guided Knowledge Compilation for Boolean Functional Synthesis

Abstract Given a specification as a Boolean relation between inputs and outputs, Boolean functional synthesis generates a function, called a Skolem function, for each output in terms of the inputs such that the specification is satisfied. In general, there may be many possibilities for Skolem functions satisfying the same specification, and criteria to pick one or the other may vary from specification to specification. In this paper, we develop a technique to represent the space of Skolem functions in a criteria-agnostic form that makes it possible to subsequently extract Skolem functions for different criteria. Our focus is on identifying such a form and on developing a compilation algorithm for this form. Our approach is based on a novel counter-example guided strategy for existentially quantifying a subset of variables from a specification in negation normal form. We implement this technique and compare our performance with those of other knowledge compilation approaches for Boolean functional synthesis, and show promising results.