Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

• 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.

Subject headings

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

Keyword

68Q17

Nullstellensatz

Pebbling

Proof complexity

Trade-offs

Publication and Content Type

art (subject category)

ref (subject category)