Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

Roderick Bloem, Nicolas Braud-Santoni, Vedad Hadzic*, Martina Seidl, Florian Lonsing, Uwe Egly

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) for obtaining a propositional abstraction of the QBF. If this formula is false, the truth value of the QBF is decided, otherwise further refinement steps are necessary. Classically, expansion-based solvers process the given formula quantifier-block wise and use one SAT solver per quantifier block. In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided and only two incremental SAT solvers are required. While our algorithm is naturally based on the ∀Exp+Res calculus that is the formal foundation of expansion-based solving, it is conceptually simpler than present recursive approaches. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.
Original languageEnglish
Pages (from-to)157-177
Number of pages21
JournalFormal Methods in System Design
Issue number2
Publication statusPublished - 23 Aug 2021


  • Decision procedures
  • Quantified Boolean formulas

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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