It is known that the satisfiability problem (SAT) can be solved with a semi-uniform family of deterministic polarizationless P systems with active membranes with non–elementary membrane division. We present a double improvement of this result by showing that the satisfiability of a quantified Boolean formula (QSAT) can be solved by a uniform family of P systems of the same kind.

We consider two-player constraint satisfaction games on systems of Boolean constraints, in which the players take turns in selecting one of the available variables and setting it to true or false, with the goal of maximising (for Player I) or minimising (for Player II) the number of satisfied constraints. Unlike in standard QBF-type variable assignment games, we impose no order in which the var...

In the past few years, we have seen significant progress in the area of Boolean satisfiability (SAT) solving and its applications. More recently, new efforts have focused on developing solvers for Quantified Boolean Formulas (QBFs). Recent QBF evaluation results show that developing practical QBF solvers is more challenging than one might expect. Even relatively small QBF problems are sometimes...

This paper presents an exact method which finds the minimum factored form of an incompletely specified Boolean function. The problem is formulated as a Quantified Boolean Formula (QBF) and is solved by general-purpose QBF solver. We also propose a novel graph structure, called an X-B (eXchanger Binary) tree, which compactly and implicitly enumerates binary trees. Leveraged by this graph structu...

One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that formula over Sylvester Hadamard matrices order 2m, Hm, can be carried out by enumerating m-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, quotient per(Hm)/22m might measure “density” high nonlinearity.

Theoretical studies show that in some combinatorial problems, there is a close relationship between classes of tractable instances and the treewidth (tw) of graphs describing their structure. In the case of satisfiability for quantified Boolean formulas (QBFs), tractable classes can be related to a generalization of treewidth, that we call quantified treewidth (twp). In this paper we investigat...

3 Contributions 3 3.1 Friedrich Slivovsky : Dependency Schemes for Quantified Boolean Formulas (Invited Talk) . . . . . . . . . . . . . . . . . . . . . 3 3.2 Olaf Beyersdorff, Leroy Chew, Meena Mahajan and Shukla Anil : Feasible Interpolation for QBF Resolution Calculi . . . 4 3.3 Valeriy Balabanov, Jie-Hong Roland Jiang and Christoph Scholl : Skolem functions computation for CEGAR based QBF so...

The possibility of solving the Quantified Boolean Formulae (QBF) problems using the SMV system is a consequence of two wellknown theoretical results: the membership of QBF to PSPACE, and the PSPACE-hardness of LTL (and therefore, of SMV). Nevertheless, such results do not imply the existence of a reduction that is also of practical utility. In this paper, we show a reduction from QBF to SMV tha...

The recently developed massively parallel satisfiability (SAT) solver HordeSAT was designed in a modular way to allow the integration of any sequential CDCL-based SAT solver in its core. We integrated the QCDCL-based quantified Boolean formula (QBF) solver DepQBF in HordeSAT to obtain a massively parallel QBF solver—HordeQBF. In this paper we describe the details of this integration and report ...

Similar to the satisfiability (SAT) problem, which can be seen to be the archetypical problem for NP, the quantified Boolean formula problem (QBF) is the archetypical problem for PSPACE. Recently, Atserias and Oliva (2014) showed that, unlike for SAT, many of the well-known decompositional parameters (such as treewidth and pathwidth) do not allow efficient algorithms for QBF. The main reason fo...