Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing

We present a new semantic gate extraction technique for propositional formulas based on interpolation. While known gate detection methods are incomplete and rely on pattern matching or simple semantic conditions, this approach can detect any definition entailed by an input formula. As an application, we consider the problem of computing unique strategy functions from Quantified Boolean Formulas (QBFs) and Dependency Quantified Boolean Formulas (DQBFs). Experiments with a prototype implementation demonstrate that functions can be efficiently extracted from formulas in standard benchmark sets, and that many of these definitions remain undetected by syntactic gate detection. We turn this into a preprocessing technique by substituting unique strategy functions for input variables and test solver performance on the resulting instances. Compared to syntactic gate detection, we see a significant increase in the number of solved QBF instances, as well as a modest increase for DQBF instances.