鸽洞公式OBDD反驳的指数下界
An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas
摘要：
哈肯证明了鸽子洞公式的每个归结反驳至少有指数大小。Groote和Zantema证明了鸽子洞公式的特定OBDD计算具有指数大小。在这里，我们表明，任何任意OBDD反驳的鸽子洞公式有一个指数的大小，太：我们证明了一个中间OBDD的大小至少是$Ω(1.025^n)$。
英文摘要：
Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least $Ω(1.025^n)$.
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