We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositional and can be solved by any SAT solver. On structured problems our implementation quantor is com...

QBF is the problem of deciding the satisfiability of quantified boolean formulae in which variables can be either universally or existentially quantified. QBF generalizes SAT (SAT is QBF under the restriction all variables are existential) and is in practice much harder to solve than SAT. One of the sources of added complexity in QBF arises from the restrictions quantifier nesting places on the...

State-of-the-art solvers for Quantified Boolean Formulas (QBF) have employed many techniques from the field of Boolean Satisfiability (SAT) including the use of Conjunctive Normal Form (CNF) in representing the QBF formula. Although CNF has worked well for SAT solvers, recent work has pointed out some inherent problems with using CNF in QBF solvers. In this paper, we describe a QBF solver, call...

We propose in this article a functional semantics for non-prenex Quantified Boolean Formulae. The proposed formalism is symetrical for validity and non-validity and allows to give different interpretations to the quantifiers. This formalism is also sufficiently flexible to allow the definition of a certificate for the search-based algorithms

In this technical report we summarize the evolution of SAT solvers implemented at the formal methods group at ETH Zürich. We start with LIMMAT and COMPSAT, which both took part in the SAT’03 SAT solver competition. From the more ambitious design of FUNEX we reach the minimal implementation of NANOSAT. We close the discussion with an overview on how our QBF solver QUANTOR can be used as a prepro...

In recent years we have seen significant progress in the area of Boolean satisfiability (SAT) solving and its applications. As a new challenge, the community is now moving to investigate whether similar advances can be made in the use of Quantified Boolean Formulas (QBF). QBF provides a natural framework for capturing problem solving and planning in multiagent settings. However, contrarily to s...

This paper proposes a novel approach to merging DL-Lite ontologies by utilising an alternative semantic characterisation instead of classical DL models. It is shown that the complexity of our merging operators is on the same level as the complexity of propositional belief merging. Moreover, a new algorithm is developed for transforming the reasoning problem of DL-Lite merging into the evaluatio...

Automatic debugging of sequential circuits has been considered a practically intractable task due to the excessive memory and run-time requirements associated with tackling industrial-size problems. This paper proposes a novel Quantified Boolean Formula (QBF) based approach for fault diagnosis in sequential circuits. A performance-driven succinct QBF encoding of the problem, coupled with the tr...

• Previously covered L, NL, PSPACE, NPSPACE – A language L is in SPACE(s(n)), where s : N → N, iff there is a deterministic TM M deciding L such that, on any input of length n, M ’s tape head visits at most c · s(n) cells over all non-input tapes, where c is a constant – Similarly, L ∈ NSPACE(s(n)) iff there is a non-deterministic TM M deciding L such that, on any input of length n and for any ...

Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are search-based. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic Q...