Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

被引：3

作者：

de Rezende, Susanna F. ^{[1
]}

Nordstrom, Jakob ^{[1
,2
]}

Meir, Or ^{[3
]}

Robere, Robert ^{[4
]}

机构：

[1] KTH Royal Inst Technol, Stockholm, Sweden

[2] Univ Copenhagen, Copenhagen, Denmark

[3] Univ Haifa, Haifa, Israel

[4] DIMACS, New Brunswick, NJ USA

来源：

34TH COMPUTATIONAL COMPLEXITY CONFERENCE (CCC 2019) | 2019年 / 137卷

基金：

以色列科学基金会; 加拿大自然科学与工程研究理事会; 美国国家科学基金会; 瑞典研究理事会;

关键词：

proof complexity; Nullstellensatz; pebble games; trade-offs; size; degree; EXPONENTIAL LOWER BOUNDS; SPACE COMPLEXITY; TIME; PROOFS; CALCULUS; SYSTEMS;

D O I：

10.4230/LIPIcs.CCC.2019.18

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

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页数：16

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