We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph G can be reversibly pebbled in time t and space s if and only if there is a Nullstellensatz refutation of the pebbling formula over G in size t + 1 and degree s (independently of the field in which the Nullstellensatz refutation is made). We use this correspondence to prove a number of strong size-degree trade-offs for Nullstellensatz, which to the best of our knowledge are the first such results for this proof system.

中文翻译：

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Nullstellensatz从大小可取的角度取舍

我们在图的可逆花絮与打扰公式的Nullstellensatz驳斥之间建立了严格的紧密关系，这表明，当且仅当在大小大于G的情况下，当扰动公式的Nullstellensatz驳斥于图G时，图G才能在时间t和空间s中可逆地卵石。t + 1和度s（独立于进行Nullstellensatz反驳的领域）。我们使用这种对应关系来证明Nullstellensatz的许多强的大小度权衡，就我们所知，这是该证明系统的首个此类结果。