Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

Susanna F. de Rezende, Jakob Nordstrom, Or Meir, Robert Robere

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

7 Citations (Scopus)
76 Downloads (Pure)

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.
Original languageEnglish
Title of host publication34th Computational Complexity Conference (CCC 2019), Proceedings
Volume137
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Publication date2019
Pages1-16
Article number18
ISBN (Electronic)978-3-95977-116-0
DOIs
Publication statusPublished - 2019
Event34th Computational Complexity Conference, CCC 2019 - New Brunswick, United States
Duration: 18 Jul 201920 Jul 2019

Conference

Conference34th Computational Complexity Conference, CCC 2019
Country/TerritoryUnited States
CityNew Brunswick
Period18/07/201920/07/2019
SponsorMicrosoft Research
SeriesLeibniz International Proceedings in Informatics, LIPIcs
Volume137
ISSN1868-8969

Keywords

  • proof complexity
  • Nullstellensatz
  • pebble games
  • trade-offs
  • size
  • degree

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