QuBIS: an (in)complete solver for quantified Boolean formulas Luca Pulina and Armando Tacchella ⋆ DIST, Universit` a di Genova, Viale Causa, 13 – 16145 Genova, Italy Luca.Pulina@unige.it - Armando.Tacchella@unige.it Abstract. In this paper we introduce QuBIS an (in)complete solver for quantified Boolean formulas (QBFs). The particularity of QuBIS is that it is not inherently incomplete, but it has the ability to surrender upon realizing that its deduction mechanism is becoming ineffective. Whenever this happens, QuBIS outputs a partial result which can be fed to a complete QBF solver for further processing. As our experiments show, not only QuBIS is competitive as an incomplete solver, but providing the output of QuBIS as an input to complete solvers can boost their performances on several instances. 1 Introduction The problem of evaluating quantified Boolean formulas (QBFs) is one of the cor- nerstones of Complexity Theory. In its most general form, it is the prototypical PSPACE-complete problem, also known as QSAT [19]. Introducing limitations on the number and the placement of alternating quantifiers, QSAT is complete for each class in the polynomial hierarchy (see, e.g., [16]). Therefore, QBFs can be seen as a low-level language in which high-level descriptions of several hard combinatorial problems can be encoded to find a solution by means of a QBF solver, and it has been shown that QBFs can provide compact propositional encodings in many automated reasoning tasks (see, e.g., [11, 1, 6]). The interest in QSAT is also witnessed by a number of QBF encodings and solvers which are made publicly available (see [8]), and by the presence of an annual competition of QBF solvers (QBFEVAL) [13]. In this paper we introduce QuBIS, an (in)complete solver for QBFs. The particularity of QuBIS is that it is not inherently incomplete, but it has the ability to surrender upon realizing that its deduction mechanism is becoming ineffective. Whenever this happens, QuBIS outputs a partial result which can be fed to a complete QBF solver for further processing. QuBIS is based on Q-resolution defined in [12] as an operation extending standard propositional resolution to QBFs represented in prenex clausal form. In particular, QuBIS uses Q-resolution to eliminate existentially quantified variables, yielding an ex- tension of the well-known Davis-Putnam [5] procedure for propositional satis- fiability (SAT). In this aspect, QuBIS is similar to the state-of-the-art solvers ⋆ The authors wish to thank MIUR for its financial support, and the reviewers who helped to improve the original manuscript.