On the complexity of propositional knowledge base revision, updates, and counterfactuals
Artificial Intelligence
The complexity of logic-based abduction
Journal of the ACM (JACM)
Resolution for quantified Boolean formulas
Information and Computation
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
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
Beyond NP: the QSAT phase transition
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Improvements to the Evaluation of Quantified Boolean Formulae
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Optimising Propositional Modal Satisfiability for Description Logic Subsumption
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
Experimental Analysis of the Computational Cost of Evaluating Quantified Boolean Formulae
AI*IA '97 Proceedings of the 5th Congress of the Italian Association for Artificial Intelligence on Advances in Artificial Intelligence
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
On evaluating decision procedures for modal logic
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Pushing the envelope: planning, propositional logic, and stochastic search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
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
QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Backjumping for quantified Boolean logic satisfiability
Artificial Intelligence
Complexity of propositional nested circumscription and nested abnormality theories
ACM Transactions on Computational Logic (TOCL)
An Effective Algorithm for the Futile Questioning Problem
Journal of Automated Reasoning
Compiling problem specification into SAT
Artificial Intelligence - Special volume on reformulation
Computational methods for database repair by signed formulae*
Annals of Mathematics and Artificial Intelligence
On quantified weighted MAX-SAT
Decision Support Systems
Local search for quantified Boolean formulas
Proceedings of the 43rd annual Southeast regional conference - Volume 1
A SAT-based solver for Q-ALL SAT
Proceedings of the 44th annual Southeast regional conference
Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae
ACM Transactions on Computational Logic (TOCL)
Boolean Functions as Models for Quantified Boolean Formulas
Journal of Automated Reasoning
Solving quantified constraint satisfaction problems
Artificial Intelligence
Value ordering for quantified CSPs
Constraints
A Unified Framework for Certificate and Compilation for QBF
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
Generalizing consistency and other constraint properties to quantified constraints
ACM Transactions on Computational Logic (TOCL)
Boolean Propagation Based on Literals for Quantified Boolean Formulae
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
The complexity of constraint satisfaction games and QCSP
Information and Computation
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
CSP properties for quantified constraints: definitions and complexity
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Generalizing Boolean satisfiability I: background and survey of existing work
Journal of Artificial Intelligence Research
Clause/term resolution and learning in the evaluation of quantified Boolean formulas
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
QCSP-solve: a solver for quantified constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Compiling problem specifications into SAT
Artificial Intelligence - Special volume on reformulation
On the expressiveness and complexity of ATL
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Bounded universal expansion for preprocessing QBF
SAT'07 Proceedings of the 10th international conference on Theory and applications 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
Monte-carlo style UCT search for boolean satisfiability
AI*IA'11 Proceedings of the 12th international conference on Artificial intelligence around man and beyond
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Partial solutions with unique completion
Reasoning, Action and Interaction in AI Theories and Systems
Local and global complete solution learning methods for QBF
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Boolean matching of function vectors with strengthened learning
Proceedings of the International Conference on Computer-Aided Design
Embedding memoization to the semantic tree search for deciding QBFs
AI'04 Proceedings of the 17th Australian joint conference on Advances in Artificial Intelligence
Automated testing and debugging of SAT and QBF solvers
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
QBF modeling: exploiting player symmetry for simplicity and efficiency
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Unified QBF certification and its applications
Formal Methods in System Design
On propositional QBF expansions and q-resolution
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Nested boolean functions as models for quantified boolean formulas
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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The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating iquantified Boolean formulae (QBFs). Algorithms for evaluation of QBFs are suitable for experimental analysis of problems that belong to a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is a generalization of the Davis–Putnam procedure for SAT and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures and report the main results of the experimental analysis. In particular, Evaluate is orders of magnitude more efficient than a nested backtracking procedure that resorts to a Davis–Putnam algorithm for handling the innermost set of quantifiers. Moreover, experiments show that randomly generated QBFs exhibit regular patterns such as phase transition and easy-hard-easy distribution.