Abstract
For quantified Boolean formulas (QBF) there are two main different approaches to solving: conflict-driven clause learning (QCDCL) and expansion solving. In this paper we compare the underlying proof systems and show that expansion systems admit strictly shorter proofs than QCDCL systems for formulas of bounded quantifier complexity, thus pointing towards potential advantages of expansion solving techniques over QCDCL solving.
Our first result shows that tree-like expansion systems allow short proofs of QBFs that are a source of hardness for QCDCL, i.e. tree-like \(\forall \textsf {Exp{+}Res}\) is strictly stronger than tree-like Q-Resolution.
In our second result we efficiently transform dag-like Q-Resolution proofs of QBFs with bounded quantifier complexity into \(\forall \textsf {Exp{+}Res}\) proofs. This is theoretical confirmation of experimental findings by Lonsing and Egly, who observed that expansion QBF solvers often outperform QCDCL solvers on instances with few quantifier alternations.
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Acknowledgements
Some of this work was done at Dagstuhl Seminar 18051, Proof Complexity. Research supported by the John Templeton Foundation and the Carl Zeiss Foundation (1st author) and EPSRC (2nd author).
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Beyersdorff, O., Chew, L., Clymo, J., Mahajan, M. (2019). Short Proofs in QBF Expansion. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_2
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