Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

Susanna F. de Rezende; Or Meir; Jakob Nordström; Robert Robere

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arXiv · 2001.02481

Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

Susanna F. de Rezende·Or Meir·Jakob Nordström·Robert Robere

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Abstract

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.

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Susanna F. de Rezende, Or Meir, Jakob Nordström, Robert Robere. 2020-01-08. Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling. https://arxiv.org/abs/2001.02481

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