@inproceedings{e932792290404271b5eed8e32799db02,
title = "Nullstellensatz size-degree trade-offs from reversible pebbling",
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.",
keywords = "Degree, Nullstellensatz, Pebble games, Proof complexity, Size, Trade-offs",
author = "{De Rezende}, {Susanna F.} and Jakob Nordstr{\"o}m and Or Meir and Robert Robere",
note = "Funding Information: Jakob Nordstr?m: was supported by the Knut and Alice Wallenberg grant KAW 2016.0066 Approximation and Proof Complexity and by the Swedish Research Council grants 621-2012-5645 and 2016-00782. Or Meir: was supported by the Israel Science Foundation (grant No. 1445/16). Robert Robere: was supported by NSERC, and also conducted part of this work at DIMACS with support from the National Science Foundation under grant number CCF-1445755. Funding Information: Funding This work was mostly carried out while the authors were visiting the Simons Institute for the Theory of Computing in association with the DIMACS/Simons Collaboration on Lower Bounds in Computational Complexity, which is conducted with support from the National Science Foundation. Susanna F. de Rezende: was supported by the Knut and Alice Wallenberg grant KAW 2016.0066 Approximation and Proof Complexity. Jakob Nordstr{\"o}m: was supported by the Knut and Alice Wallenberg grant KAW 2016.0066 Approximation and Proof Complexity and by the Swedish Research Council grants 621-2012-5645 and 2016-00782. Or Meir: was supported by the Israel Science Foundation (grant No. 1445/16). Robert Robere: was supported by NSERC, and also conducted part of this work at DIMACS with support from the National Science Foundation under grant number CCF-1445755. Publisher Copyright: {\textcopyright} Susanna F. de Rezende, Jakob Nordstr{\"o}m, Or Meir, and Robert Robere; licensed under Creative Commons License CC-BY 34th Computational Complexity Conference (CCC 2019).; 34th Computational Complexity Conference, CCC 2019 ; Conference date: 18-07-2019 Through 20-07-2019",
year = "2019",
month = jul,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.CCC.2019.18",
language = "American English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "18:1–18:16",
editor = "Amir Shpilka",
booktitle = "34th Computational Complexity Conference, CCC 2019",
address = "Germany",
}