The satisfiability problem (SAT) [6] consists in finding a truth assignment that satisfies a wellformed Boolean expression. An instance of the SAT problem is defined by a set of boolean variables (also called atoms) X = {x1, ..., xn} and a boolean formula φ: {0, 1}n → {0, 1}. A literal is a variable or its negation. A (truth) assignment is a function v:X → {0, 1}. The formula is said to be sati...

This paper considers Boolean formulae and their simulations by bounded width branching programs. It is shown that every balanced Boolean formula of size s can be simulated by a constant width (width 5) branching program of length s 1.81 l.... A lower bound for the translational cost from formulae to permutation branching programs is also presented. Key words, branching programs, Boolean formula...

We give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match t...

This paper describes a technique for translating bounded propositional reachability problems, such as Planning, into Quantified Boolean Formulae (QBF). The key feature of this translation is that the problem, and the resultant encoding is only partially grounded. The technique is applicable to other SAT or QBF encodings as an additional improvement, potentially reducing the size of the resultin...

The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be Σ2 -complete and indeed appears as an open problem in Garey and Johnson [GJ79]. The depth-2 variant was only shown to be Σ2 -complete in 1998 [Uma98], and even resolving the complexity of the depth-3 version has been mentioned as a ...

Trivial truth and backjumping are two optimization techniques that have been proposed for deciding quantified boolean formulas (QBFs) satisfiability. Both these techniques can greatly improve the overall performance of a QBF solver, but they are the expression of opposite philosophies. On one hand, trivial truth is a “look-ahead” policy: it is applied when descending the search tree to (try to)...

In this note we describe STRUQS, a solver that approaches the problem of reasoning with quantified Boolean formulas (QBFs) by combining search and resolution, and by switching between them according to structural properties of QBFs. Here it is described the version submitted to the competitive evaluation of QBF solvers 2010 (QBFEVAL’10), and it is based on the work presented in [1], and extende...

The practical use of Quantified Boolean Formulas (QBFs) often calls for more than solving the validity problem QBF. For this reason we investigate the corresponding function problems whose expected outputs are policies. QBFs which do not evaluate to true do not have any solution policy, but can be of interest nevertheless; for handling them, we introduce a notion of partial policy. We focus on ...

Similar to most state-of-the-art Boolean Satisfiability (SAT) solvers, all contemporary Quantified Boolean Formula (QBF) solvers require inputs to be in the Conjunctive Normal Form (CNF). Most of them also store the QBF in CNF internally for reasoning. In order to use these solvers, arbitrary Boolean formulas have to be transformed into equi-satisfiable formulas in Conjunctive Normal Form by in...

The aim of the paper to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard problem. Given an E3-CNF Boolean formula, the aim of the MAX-E3-SAT problem is to find the variable assignment that maximizes the number of satisfied clauses. The pr...