A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Resolution for quantified Boolean formulas
Information and Computation
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
An algorithm to evaluate quantified Boolean formulae
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Checking equivalence for partial implementations
Proceedings of the 38th annual Design Automation Conference
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
Journal of Automated Reasoning
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Bounded Model Construction for Monadic Second-Order Logics
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Minimizing the Number of Clauses by Renaming
Proceedings of the 10th International Conference on Automated Deduction
Conflict driven learning in a quantified Boolean Satisfiability solver
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Learning for quantified boolean logic satisfiability
Eighteenth national conference on Artificial intelligence
Resolution decision procedures
Handbook of automated reasoning
Backjumping for quantified Boolean logic satisfiability
Artificial Intelligence
SAT-based planning in complex domains: concurrency, constraints and nondeterminism
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Constructing conditional plans by a theorem-prover
Journal of Artificial Intelligence Research
Backjumping for quantified Boolean logic satisfiability
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
QBF reasoning on real-world instances
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Solving quantified constraint satisfaction problems
Artificial Intelligence
QuBIS: An (In)complete Solver for Quantified Boolean Formulas
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Treewidth: A Useful Marker of Empirical Hardness in Quantified Boolean Logic Encodings
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Unified Framework for Certificate and Compilation for QBF
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
PaQuBE: Distributed QBF Solving with Advanced Knowledge Sharing
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
A structural approach to reasoning with quantified Boolean formulas
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Minimal module extraction from DL-lite ontologies using QBF solvers
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Evaluating and certifying QBFs: A comparison of state-of-the-art tools
AI Communications
Hard QBF Encodings Made Easy: Dream or Reality?
AI*IA '09: Proceedings of the XIth International Conference of the Italian Association for Artificial Intelligence Reggio Emilia on Emergent Perspectives in Artificial Intelligence
An overview of AI research in Italy
Artificial intelligence
Learning to integrate deduction and search in reasoning about quantified boolean formulas
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Logic-based ontology comparison and module extraction, with an application to DL-Lite
Artificial Intelligence
An Empirical Study of QBF Encodings: from Treewidth Estimation to Useful Preprocessing
Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Abstraction-based algorithm for 2QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Failed literal detection for QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Resolution proofs and Skolem functions in QBF evaluation and applications
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
sQueezeBF: an effective preprocessor for QBFs based on equivalence reasoning
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Integrating dependency schemes in search-based QBF solvers
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Encoding techniques, craig interpolants and bounded model checking for incomplete designs
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
The seventh QBF solvers evaluation (QBFEVAL’10)
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Unified QBF certification and its applications
Formal Methods in System Design
Parallel QBF Solving with Advanced Knowledge Sharing
Fundamenta Informaticae - RCRA 2009 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Contributions to the theory of practical quantified boolean formula solving
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
ALLQBF solving by computational learning
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Verification of partial designs using incremental QBF solving
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
On propositional QBF expansions and q-resolution
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Recovering and utilizing partial duality in QBF
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Efficient clause learning for quantified boolean formulas via QBF pseudo unit propagation
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Minimizing models for tseitin-encoded SAT instances
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Henkin quantifiers and Boolean formulae: A certification perspective of DQBF
Theoretical Computer Science
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Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called "Q-resolution", is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs -based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.