An AIG-Based QBF-solver using SAT for preprocessing

Abstract

In this paper we present a solver for Quantified Boolean Formulas (QBFs) which is based on And-Inverter Graphs (AIGs). We use a new quantifier elimination method for AIGs, which heuristically combines cofactor-based quantifier elimination with quantification using BDDs and thus benefits from the strengths of both data structures. Moreover, we present a novel SAT-based method for preprocessing QBFs that is able to efficiently detect variables with forced truth assignments, allowing for an elimination of these variables from the input formula. We describe the used algorithm which heavily relies on the incremental features of modern SATsolvers. Experimental results demonstrate that our preprocessing method can significantly improve the performance of QBF preprocessing and thus is able to accelerate the overall solving process when used in combination with state-of-the-art QBF-solvers. In particular, we integrated the preprocessing technique as well as the quantifier elimination method into the QBF-solver AIGSolve, allowing it to outperform state-of-the-art solvers.

Failed Literal Detection for QBF

“…This allows for incremental SAT solving and optimizations based on CNF-models to reduce the number of SAT solver calls like in [21]. Additionally, unit clauses learnt by PicoSAT are propagated using QBF-specific QBCP rules within QxBF.…”

“…This has already been applied to QBF [21]. We include it here as a reference for our approaches introduced in Sections 4 and 5.…”

“…When combining Propositions 1 and 2, a SAT solver can be used to check if a unit clause is implied by the CNF part of a PCNF for QBF preprocessing [21].…”

“…In order to overcome this drawback, several approaches for preprocessing PCNFs have been suggested. Some were ported from SAT to QBF such as binary clause reasoning, equivalence detection and variable elimination by resolution or expansion [2,5,6,11,21,25,26].…”

“…In [21] a SAT solver was applied to detect necessary assignments of the CNF part of PCNFs. We consider the same approach mainly for reference (Section 3) but also show that it is incomparable to our FL approaches (Section 6).…”