The IP theorem, which asserts that IP = PSPACE (Lund et. al., and Shamir, in J. ACM 39(4)), is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The intuition that underlies the use of polynomials is commonly explained by the fact that polynomial...

Dependency Quantified Boolean Formulas (DQBF) comprise the set of propositional formulas which can be formulated by adding Henkin quantifiers to Boolean logic. We are not aware of any published attempt in solving this class of formulas in practice. However with DQBF being NEXPTIME-complete, efficient ways of solving it would have many practical applications. In this paper we describe a DPLL-sty...

We establish a framework to integrate propositional logic with first-order logic. This is done in such a way that it optionally appears either as first-order logic over a Boolean algebra or as propositional logic including Boolean quantification. We describe and prove complexity bounds for extended quantifier elimination by virtual substitution for our theory. This extended quantifier eliminati...

In spite of the close connection between the evaluation of quantified Boolean formulas (QBF) and propositional satisfiability (SAT), tools and techniques which exploit structural properties of SAT instances are known to fail for QBF. This is especially true for the structural parameter treewidth, which has allowed the design of successful algorithms for SAT but cannot be straightforwardly appli...

Search based solvers for Quantified Boolean Formulas (QBF) have adapted the SAT solver techniques of unit propagation and clause learning to prune falsifying assignments. The technique of cube learning has been developed to help them prune satisfying assignments. Cubes, however, have not been able to achieve the same degree of effectiveness as clauses. In this paper we demonstrate how a circuit...

We present DepQBF 0.1, a new search-based solver for quantified boolean formulae (QBF). It integrates compact dependency graphs to overcome the restrictions imposed by linear quantifier prefixes of QBFs in prenex conjunctive normal form (PCNF). DepQBF 0.1 was placed first in the main track of QBFEVAL’10 in a score-based ranking. We provide a general system overview and describe selected orthogo...

Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi that this problem is PSPACE-complete even fo...

Many reasoning task and combinatorial problems exhibit symmetries. Exploiting such symmetries has been proved useful in reducing the search space. In this paper, a formal approach for symmetry breaking in quantified boolean formula is proposed. It make use of a new efficient technique for encoding the additional symmetry predicates in prenex clausal form. The new asymmetric formula is equivalen...

In computer science, often computational problems can be transformed into communication problems. The most illustrative example is probably the evaluation of a function via a Boolean formula. The correspondence to an equivalent communication game is as follows. A Boolean formula computing the function value g(x1, . . . , xk) can be represented by a binary tree. The leaves are labeled with varia...

This paper presents a method to automati ally prove statements from primitive re ursive arithmeti . The method repla es logi al formulas by boolean expressions. A orre tness proof is onstru ted, whi h states that the original formula is derivable, if and only if the boolean expression equals true. Be ause the boolean expression redu es to true, the onversion rule yields a trivial proof of the e...