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Shortening QBF Proofs with Dependency Schemes

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Theory and Applications of Satisfiability Testing – SAT 2017 (SAT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

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Abstract

We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014 [30]. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of inprocessing. Formalising this notion, we introduce a new calculus in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation.

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Notes

  1. 1.

    In practice, the dual notion of (in)dependence of universals on existentials is equally important.

  2. 2.

    The term ‘full exhibition’ was coined in [2]. The concept itself and the term ‘\(\mathcal {D}\)-model’ originate from [29].

  3. 3.

    We prove this statement formally in Subsect. 5.2 (Lemma 14).

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Correspondence to Joshua Blinkhorn .

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Blinkhorn, J., Beyersdorff, O. (2017). Shortening QBF Proofs with Dependency Schemes. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_17

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