On the virtue of succinct proofs: Amplifying communication complexity hardness to time-space trade-offs in proof complexity

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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} n such that: • The formulas F n have size Θ(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.


Externa organisationer
  • ETH Zürich
  • KTH Royal Institute of Technology

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)


Titel på värdpublikationSTOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
FörlagAssociation for Computing Machinery (ACM)
Antal sidor15
ISBN (tryckt)9781450312455
StatusPublished - 2012
Peer review utfördJa
Externt publiceradJa
Evenemang44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, USA
Varaktighet: 2012 maj 192012 maj 22


NamnProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (tryckt)0737-8017


Konferens44th Annual ACM Symposium on Theory of Computing, STOC '12
OrtNew York, NY