Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving.

中文翻译：

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在 QBF 证明中构建策略

策略提取对于量化布尔公式 (QBF) 而言，在求解和证明复杂性方面都非常重要。到目前为止，在 QBF 文献中，策略提取是从证明中通过算法执行的。在这里，我们设计了第一个 QBF 系统，其中（部分）策略内置于证明中，并通过简单操作和推导分段构建。这有几个优点：（1）我们的微积分线有明确的语义，因为它们伴随着语义对象；(2) 部分策略被简洁地表示（与之前的一些方法相反）；(3) 我们的微积分设计有策略抽取；(4) 部分策略允许新的声音推理步骤，这些步骤在以前的中央 QBF 演算中是不允许的，例如 Q-Resolution 和长距离 Q-Resolution。最后一项 (4) 使我们能够展示我们的新系统与先前研究的无约简长距离分辨率演算之间的指数分离。我们的方法也自然地提升到依赖 QBF（DQBF），在那里它为 DQBF 产生了第一个健全和完整的 CDCL 式微积分，从而为基于 CDCL 的 DQBF 求解开辟了未来的途径。