An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
Journal of Automated Reasoning
Extracting certificates from quantified boolean formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A first step towards a unified proof checker for QBF
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Equivalence models for quantified boolean formulas
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A uniform approach for generating proofs and strategies for both true and false QBF formulas
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Unified QBF certification and its applications
Formal Methods in System Design
Resolution-based certificate extraction for QBF
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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Nested Boolean functions or Boolean programs are an alternative to the quantified Boolean formula (QBF) characterization of polynomial space. The idea is to start with a set of Boolean functions given as propositional formulas and to define new functions as compositions or instantiations of previously defined ones. We investigate the relationship between function instantiation and quantification and present a compact representation of models and countermodels of QBFs with and without free variables as nested Boolean functions. The representation is symmetric with respect to Skolem models and Herbrand countermodels. For a formula with free variables, it can describe both kinds of models simultaneously in one complete equivalence model which can be Skolem or Herbrand depending on actual assignments to the free variables.