Shortening QBF Proofs with Dependency Schemes
نویسندگان
چکیده
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 inprocessing. Formalising this notion, we introduce a new calculus in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation.
منابع مشابه
Dependency Schemes in QBF Calculi: Semantics and Soundness
We study the parametrization of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on ‘exhibition’ by QBF models, and use it to define a property of dependency schemes called full exhibition. We prove tha...
متن کاملDependency Schemes and Search-Based QBF Solving: Theory and Practice
The logic of quantified Boolean formulae (QBF) extends propositional logic with universal quantification over propositional variables. The presence of universal quantifiers in QBF does not add expressiveness, but often allows for more compact encodings of problems. From a theoretical point of view, the decision problems of propositional logic (SAT) and QBF are NP-complete and PSPACE-complete, r...
متن کاملEfficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation
Recent solvers for quantified boolean formulas (QBF) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. Recently, an exponential worst case for this procedure has been shown by Van Gelder (CP 2012). That paper introduced QBF Pseudo Unit Propagation (QPUP) for non-tautological clause learning in a limited sett...
متن کاملLong Distance Q-Resolution with Dependency Schemes
Resolution proof systems for quantified Boolean formulas (QBFs) provide a formal model for studying the limitations of state-of-the-art search-based QBF solvers that use these systems to generate proofs. We study a proof system that combines two proof systems supported by the solver DepQBF: Q-resolution with generalized universal reduction according to a dependency scheme and long distance Q-re...
متن کاملDependency Schemes for DQBF
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017