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Proof Complexity of Symbolic QBF Reasoning
arXiv - CS - Logic in Computer Science Pub Date : 2021-04-06 , DOI: arxiv-2104.02563
Stefan Mengel, Friedrich Slivovsky

We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such admit short proofs of formulas of bounded path-width and quantifier complexity. As a consequence, we obtain exponential separations from standard clausal proof systems, specifically (long-distance) QU-Resolution and IR-Calc. We further develop a lower bound technique for symbolic QBF proof systems based on strategy extraction that lifts known lower bounds from communication complexity. This allows us to derive strong lower bounds against symbolic QBF proof systems that are independent of the variable ordering of the underlying OBDDs, and that hold even if the proof system is allowed access to an NP-oracle.

中文翻译:

QBF符号推理的证明复杂性

我们介绍和研究在有序二元决策图(OBDD)上运行的量化布尔公式(QBF)的符号证明系统。这些系统捕获执行符号量化符消除的QBF求解器,因此可以接受有限路径宽度和量化器复杂度公式的简短证明。结果,我们从标准子句证明系统中获得了指数间隔,特别是(远距离)QU分辨率和IR-Calc。我们进一步基于策略提取为符号QBF证明系统开发了下界技术,该技术从通信复杂性中提升了已知的下界。这使我们能够针对符号QBF证明系统得出强大的下界,该系统与底层OBDD的变量顺序无关,即使允许该证明系统访问NP-oracle,它也保持不变。
更新日期:2021-04-08
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