Clauses Versus Gates in CEGAR-Based 2QBF Solving

Valeriy Balabanov, Jie-Hong Roland Jiang, Alan Mishchenko, Christoph Scholl

Abstract: 2QBF is a special case of general quantified Boolean formulae (QBF). It is limited to just two quantification levels, i.e., to a form ∀X∃Y.φ. Despite this limitation it applies to a wide range of applications, e.g., to artificial intelligence, graph theorysynthesis, etc.. Recent research showed that CEGAR-based methodsgive a performance boost to QBF solving (e.g, compared to QDPLL). Conjunctive normal form (CNF) is a commonly accepted representation for both SAT and QBF problems; however, it does not reflect the circuit structure that might be present in the problem. Existing attempts of extracting this structure from CNF and using it in 2QBF context do not show advantages over CNF based 2QBF solvers. In this work we introduce a new workflow for 2QBF, containing a new semantic circuit extraction algorithm and a CEGAR-based 2QBF solver that uses circuit structure and is improved by a so-called “cofactor sharing” heuristics. We evaluate the proposed methodology on a range of benchmarks and show the practicality of the new approach.