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We propose two novel approaches for using Counterexample-Guided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver.(More)
A set of constraints that cannot be simultaneously satisfied is over-constrained. Minimal relaxations and minimal explanations for over-constrained problems find many practical uses. For Boolean formulas, minimal relaxations of over-constrained problems are referred to as Minimal Correction Subsets (MCSes). MCSes find many applications, including the(More)
A mechanically formalized feature modeling meta-model is presented. This theory is a generic higher-order formalization of a mathematical model synthesizing several feature modeling approaches found in the literature. This meta-model supports not only a better understanding of the various approaches to feature modeling, but also supports reasoning about and(More)
Over the years, proof systems for propositional satisfiability (SAT) have been extensively studied. Recently, proof systems for quantified Boolean formulas (QBFs) have also been gaining attention. Q-resolution is a calculus enabling producing proofs from DPLL-based QBF solvers. While DPLL has become a dominating technique for SAT, QBF has been tackled by(More)
This article introduces and studies a proof system ∀Exp+Res that enables us to refute quantified Boolean formulas (QBFs). The system ∀Exp+Res operates in two stages: it expands all universal variables through conjunctions and refutes the result by propositional resolution. This approach contrasts with the Q-resolution calculus, which enables refuting QBFs(More)
Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two(More)
A configuration process is about finding a configuration, a setting, that satisfies the requirements given by the user and constraints imposed by the domain. Feature models are used to record product domains and constraints imposed on individual products. As such constraints are in practice of complex nature, it is desirable to perform the configuration(More)
Our feature configuration tool S 2 T 2 Configurator integrates (1) a visual interactive representation of the feature model and (2) a formal reasoning engine that calculates consequences of the user's actions and provides formal explanations. The tool's software architecture is designed as a chain of components, which provide mappings between visual(More)