Paper Info
Title
On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity
Abstract
An active line of research in proof complexity over the last decade has been the study of proof space and trade-offs between size and space. Such questions were originally motivated by practical SAT solving, but have also led to the development of new theoretical concepts in proof complexity of intrinsic interest and to results establishing nontrivial relations between space and other proof complexity measures. By now, the resolution proof system is fairly well understood in this regard, as witnessed by a sequence of papers leading up to [Ben-Sasson and Nordstrom 2008, 2011] and [Beame, Beck, and Impagliazzo 2012]. However, for other relevant proof systems in the context of SAT solving, such as polynomial calculus (PC) and cutting planes (CP), very little has been known. Inspired by [BN08, BN11], we consider CNF encodings of so-called pebble games played on graphs and the approach of making such pebbling formulas harder by simple syntactic modifications. We use this paradigm of hardness amplification to make progress on the relatively longstanding open question of proving time-space trade-offs for PC and CP. Namely, we exhibit a family of modified pebbling formulas {F_n} such that: - The formulas F_n have size O(n) and width O(1). - They have proofs in length O(n) in resolution, which generalize to both PC and CP. - Any refutation in CP or PCR (a generalization of PC) in length L and space s must satisfy s log L ≈ √[4]{n}. A crucial technical ingredient in these results is a new two-player communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be of independent interest.
Year
DOI
Venue
2012
10.1145/2213977.2214000
STOC
Keywords
Field
DocType
proof space,width o,size o,independent interest,relevant proof system,succinct proof,resolution proof system,proof complexity measure,new two-player communication complexity,length o,communication complexity hardness,proof complexity,trade offs,space,computer science,satisfiability,length,resolution,communication complexity,lower bound,size,pcr,cutting plane
Probabilistically checkable proof,Discrete mathematics,Graph,Combinatorics,Upper and lower bounds,Communication complexity,Space trade,Mathematical proof,Proof complexity,Polynomial calculus,Mathematics
Conference
Citations 
PageRank 
References 
20
0.78
51
Authors
2
Name
Order
Citations
PageRank
Trinh Huynh1442.53
Jakob Nordstrom2422.10