Solving QBF with Combined Conjunctive and Disjunctive Normal Form
نویسنده
چکیده
Similar to most state-of-the-art Boolean Satisfiability (SAT) solvers, all contemporary Quantified Boolean Formula (QBF) solvers require inputs to be in the Conjunctive Normal Form (CNF). Most of them also store the QBF in CNF internally for reasoning. In order to use these solvers, arbitrary Boolean formulas have to be transformed into equi-satisfiable formulas in Conjunctive Normal Form by introducing additional variables. In this paper, we point out an inherent limitation of this approach, namely the asymmetric treatment of satisfactions and conflicts. This deficiency leads to artificial increase of search space for QBF solving. To overcome the limitation, we propose to transform a Boolean formula into a combination of an equisatisfiable CNF formula and an equi-tautological DNF formula for QBF solving. QBF solvers based on this approach treat satisfactions and conflicts symmetrically, thus avoiding the exploration of unnecessary search space. A QBF solver called IQTest is implemented based on this idea. Experimental results show that it significantly outperforms existing QBF solvers.
منابع مشابه
ALLQBF Solving by Computational Learning
In the last years, search-based QBF solvers have become essential for many applications in the formal methods domain. The exploitation of their reasoning efficiency has however been restricted to applications in which a “satisfiable/unsatisfiable” answer or one model of an open quantified Boolean formula suffices as an outcome, whereas applications in which a compact representation of all model...
متن کاملQBF Modeling: Exploiting Player Symmetry for Simplicity and Efficiency
Quantified Boolean Formulas (QBFs) present the next big challenge for automated propositional reasoning. Not surprisingly, most of the present day QBF solvers are extensions of successful propositional satisfiability algorithms (SAT solvers). They directly integrate the lessons learned from SAT research, thus avoiding re-inventing the wheel. In particular, they use the standard conjunctive norm...
متن کاملComplete Problems of Propositional Logic for the Exponential Hierarchy
Large complexity classes, like the exponential time hierarchy, received little attention in terms of finding complete problems. In this work a generalization of propositional logic is investigated which fills this gap with the introduction of Boolean higher-order quantifiers or equivalently Boolean Skolem functions. This builds on the important results of Wrathall and Stockmeyer regarding compl...
متن کاملQ-Resolution with Generalized Axioms
Q-resolution is a proof system for quantified Boolean formulas (QBFs) in prenex conjunctive normal form (PCNF) which underlies search-based QBF solvers with clause and cube learning (QCDCL). With the aim to derive and learn stronger clauses and cubes earlier in the search, we generalize the axioms of the Q-resolution calculus resulting in an exponentially more powerful proof system. The general...
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 کامل