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DOI: 10.4230/LIPIcs.CCC.2019.18
URN: urn:nbn:de:0030-drops-108403
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10840/
de Rezende, Susanna F. ; Nordström, Jakob ; Meir, Or ; Robere, Robert
Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling
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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.
BibTeX - Entry
@InProceedings{derezende_et_al:LIPIcs:2019:10840,
author = {Susanna F. de Rezende and Jakob Nordstr{\"o}m and Or Meir and Robert Robere},
title = {{Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling}},
booktitle = {34th Computational Complexity Conference (CCC 2019)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-116-0},
ISSN = {1868-8969},
year = {2019},
volume = {137},
editor = {Amir Shpilka},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10840},
URN = {urn:nbn:de:0030-drops-108403},
doi = {10.4230/LIPIcs.CCC.2019.18},
annote = {Keywords: proof complexity, Nullstellensatz, pebble games, trade-offs, size, degree}
}
| Keywords: | proof complexity, Nullstellensatz, pebble games, trade-offs, size, degree | |
| Seminar: | 34th Computational Complexity Conference (CCC 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 16.07.2019 |
