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QRAT Polynomially Simulates \(\forall \text {-Exp+Res}\)

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Theory and Applications of Satisfiability Testing – SAT 2019 (SAT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11628))

Abstract

The proof system \(\forall \text {-Exp+Res}\) formally captures expansion-based solving of quantified Boolean formulas (QBFs) whereas the \(\mathsf {QRAT}\) proof system captures QBF preprocessing. From previous work it is known that certain families of formulas have short proofs in \(\mathsf {QRAT}\) but not in \(\forall \text {-Exp+Res}\). However, it was not known if the two proof systems were incomparable (i.e., if there also existed QBFs with short \(\forall \text {-Exp+Res}\) proofs but without short \(\mathsf {QRAT}\) proofs), or if \(\mathsf {QRAT}\) polynomially simulates \(\forall \text {-Exp+Res}\). We close this gap of the QBF-proof-complexity landscape by presenting a polynomial simulation of \(\forall \text {-Exp+Res}\) in \(\mathsf {QRAT}\). Our simulation shows how definition introduction combined with extended-universal reduction can mimic the concept of universal expansion.

This work has been supported by the Austrian Science Fund (FWF) projects W1255-N23 and S11408-N23 and the LIT AI Lab funded by the State of Upper Austria.

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Kiesl, B., Seidl, M. (2019). QRAT Polynomially Simulates \(\forall \text {-Exp+Res}\). 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_13

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  • DOI: https://doi.org/10.1007/978-3-030-24258-9_13

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