We devise a new technique to prove lower bounds for the proof size in resolutiontype calculi for quantified Boolean formulas (QBF). The new technique applies to the strong expansion system IR-calc and thereby also to the most studied QBF system Q-Resolution. Our technique exploits a clear semantic paradigm, showing the hardness of a QBF family by demonstrating that (1) the formulas require larg...

Dependency schemes allow to identify variable independencies in QBFs or DQBFs. For QBF, several dependency schemes have been proposed, which differ in the number of independencies they are able to identify. In this paper, we analyze the spectrum of dependency schemes that were proposed for QBF. It turns out that only some of them are sound for DQBF. For the sound ones, we provide a correctness ...

During the recent years, the development of tools for deciding Quantified Boolean Formulas (QBFs) has been accompanied by a steady supply of real-world instances, i.e., QBFs originated by translations from application domains. Instances of this kind showed to be challenging for current state-of-the-art QBF solvers, while the ability to deal effectively with them is necessary to foster adoption ...

Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver calls. This hinders the independent comparison of different solvers, particularly when the application program is not available. As a remedy, we present an appro...

A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions. There are two methodologies in CEGAR based QBF solving techniques, one that is based on a refinement loop that builds partial expansions and a more recent one that is based on the communication of satisfied clauses. Despite their algorithmic similarity, their p...

Modern solvers for quantified Boolean formulas (QBF) not only decide the satisfiability of a formula, but also return a set of Skolem functions representing a model for a true QBF. Unfortunately, in combination with a preprocessor this ability is lost for many preprocessing techniques. A preprocessor rewrites the input formula to an equi-satisfiable formula which is often easier to solve than t...

Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this paper, three common variations of games are applied to create seven new games: whether each player is restricted to where they may play, which values they may set...

We revisit the interactive consistency problem introduced by Pease, Shostak and Lamport. We first show that their algorithm does not achieve interactive consistency if faults are transient, even if faults are non-malicious. We then present an algorithm that achieves interactive consistency in presence of nonmalicious, asymmetric and transient faults, but only under an additional guaranteed dela...

A large number of applications can be represented by quantified Boolean formulas (QBF). Although evaluating QBF is NP-hard and thus very difficult, there has been significant progress in the development of QBF solvers. These solvers require the quantified Boolean formula to be in a standard format. We have encountered a large class of problems whose representation as QBF is not in that standard...

Previous work has shown that circuit representations can be exploited in QBF solvers to obtain useful performance improvements. In this paper we examine some additional techniques for exploiting a circuit representations. We discuss the techniques of propagating a dual set of values through the circuit, conversion from simple negation normal form to a more optimized circuit representation, and ...