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Strategy Extraction by Interpolation

Author Friedrich Slivovsky

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Friedrich Slivovsky
  • Department of Computer Science, University of Liverpool, UK

Funding

Vienna Science and Technology Fund (WWTF) grant 10.47379/ICT19060.

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Friedrich Slivovsky. Strategy Extraction by Interpolation. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAT.2024.28

Abstract

In applications, QBF solvers are often required to generate strategies. This typically involves a process known as strategy extraction, where a Boolean circuit encoding a strategy is computed from a proof. It has previously been observed that Craig interpolation in propositional logic can be seen as a special case of QBF strategy extraction. In this paper we explore this connection further and show that, conversely, any strategy for a false QBF corresponds to a sequence of interpolants in its complete (Herbrand) expansion. Inspired by this correspondence, we present a new strategy extraction algorithm for the expansion-based proof system Exp+Res. Its asymptotic running time matches the best known bound of O(mn) for a proof with m lines and n universally quantified variables. We report on experiments comparing this algorithm with a strategy extraction algorithm based on combining partial strategies, as well as with round-based strategy extraction.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
Keywords
  • QBF
  • Expansion
  • Strategy Extraction
  • Interpolation

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References

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