Validation of QBF Encodings with Winning Strategies

Authors Irfansha Shaik , Maximilian Heisinger , Martina Seidl , Jaco van de Pol

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Author Details

Irfansha Shaik
  • Aarhus University, Denmark
Maximilian Heisinger
  • Johannes Kepler Universität Linz, Austria
Martina Seidl
  • Johannes Kepler Universität Linz, Austria
Jaco van de Pol
  • Aarhus University, Denmark

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Irfansha Shaik, Maximilian Heisinger, Martina Seidl, and Jaco van de Pol. Validation of QBF Encodings with Winning Strategies. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 24:1-24:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


When using a QBF solver for solving application problems encoded to quantified Boolean formulas (QBFs), mainly two things can potentially go wrong: (1) the solver could be buggy and return a wrong result or (2) the encoding could be incorrect. To ensure the correctness of solvers, sophisticated fuzzing and testing techniques have been presented. To ultimately trust a solving result, solvers have to provide a proof certificate that can be independently checked. Much less attention, however, has been paid to the question how to ensure the correctness of encodings. The validation of QBF encodings is particularly challenging because of the variable dependencies introduced by the quantifiers. In contrast to SAT, the solution of a true QBF is not simply a variable assignment, but a winning strategy. For each existential variable x, a winning strategy provides a function that defines how to set x based on the values of the universal variables that precede x in the quantifier prefix. Winning strategies for false formulas are defined dually. In this paper, we provide a tool for validating encodings using winning strategies and interactive game play with a QBF solver. As the representation of winning strategies can get huge, we also introduce validation based on partial winning strategies. Finally, we employ winning strategies for testing if two different encodings of one problem have the same solutions.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Artificial intelligence
  • Theory of computation → Logic and verification
  • QBF
  • Validation
  • Winning Strategy
  • Equivalence
  • Certificates


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