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Models and Counter-Models of Quantified Boolean Formulas (Invited Talk)

Author Martina Seidl

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Martina Seidl
  • Johannes Kepler University Linz, Austria

Funding

Parts of this work were supported by the LIT AI Lab founded by the State of Upper Austria.

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Martina Seidl. Models and Counter-Models of Quantified Boolean Formulas (Invited Talk). In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 1:1-1:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAT.2024.1

Abstract

Because of the duality of universal and existential quantification, quantified Boolean formulas (QBF), the extension of propositional logic with quantifiers over the Boolean variables, have not only solutions in terms of models for true formulas like in SAT. Also false QBFs have solutions in terms of counter-models. Both models and counter-models can be represented as certain binary trees or as sets of Boolean functions reflecting the dependencies among the variables of a formula. Such solutions encode the answers to application problems for which QBF solvers are employed like the plan for a planning problem or the error trace of a verification problem. Therefore, models and counter-models are at the core of theory and practice of QBF solving. In this invited talk, we survey approaches that deal with models and counter-models of QBFs and identify some open challenges.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
Keywords
  • Quantified Boolean Formula
  • Solution Extraction
  • Solution Counting

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