Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

Susanna F. De Rezende, Or Meir, Jakob Nordström, Robert Robere

Research output: Contribution to journalArticlepeer-review


We establish an exactly tight relation between reversiblepebblings 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 formulaover G in size t + 1 and degree s (independently of the field in whichthe Nullstellensatz refutation is made). We use this correspondenceto prove a number of strong size-degree trade-offs for Nullstellensatz,which to the best of our knowledge are the first such results for thisproof system.

Original languageEnglish
Article number4
JournalComputational Complexity
Issue number1
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • 68Q17
  • Nullstellensatz
  • Pebbling
  • Proof complexity
  • Trade-offs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Mathematics
  • Computational Theory and Mathematics
  • Computational Mathematics


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