Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling
Computational Complexity
2020-01-09 v1
Abstract
We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph can be reversibly pebbled in time and space if and only if there is a Nullstellensatz refutation of the pebbling formula over in size and degree (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.
Cite
@article{arxiv.2001.02481,
title = {Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling},
author = {Susanna F. de Rezende and Or Meir and Jakob Nordström and Robert Robere},
journal= {arXiv preprint arXiv:2001.02481},
year = {2020}
}