Small Resolution Proofs for QBF using Dependency Treewidth
نویسندگان
چکیده
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 applied to QBF since it does not take into account the interdependencies between quantified variables. In this work we introduce and develop dependency treewidth, a new structural parameter based on treewidth which allows the efficient solution of QBF instances. Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF. We augment our results by developing algorithms for computing the decompositions that are required to use the parameter. Digital Object Identifier 10.4230/LIPIcs...
منابع مشابه
Shortening QBF Proofs with Dependency Schemes
We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014 [30]. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of in...
متن کاملFormulas with Large Weight: a New Technique for Genuine QBF Lower Bounds
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...
متن کاملExtracting and Checking Q-Resolution Proofs from a State-Of-The-Art QBF-Solver
The logic of Quantified Boolean Formulas (QBF) is an extension of propositional logic and provides compact encodings of real world problems in various fields of application, e.g., formal verification, reasoning and artificial intelligence. In recent years, the development of efficient decision procedures for QBF has progressed considerably. However, most current state-of-the-art QBF-solvers ret...
متن کاملSTRUQS: A Structural QBF Solver
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...
متن کاملLong-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving
Strategies (and certificates) for quantified Boolean formulas (QBFs) are of high practical relevance as they facilitate the verification of results returned by QBF solvers and the generation of solutions to problems formulated as QBFs. State of the art approaches to obtain strategies require traversing a Q-resolution proof of a QBF, which for many real-life instances is too large to handle. In ...
متن کامل