Static data structure lower bounds imply rigidity

Zeev Dvir, Alexander Golovnev, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

We show that static data structure lower bounds in the group (linear) model imply semi-explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of t ≥ ω(log2 n) on the cell-probe complexity of linear data structures in the group model, even against arbitrarily small linear space (s = (1 + ε)n), would already imply a semi-explicit (PNP) construction of rigid matrices with significantly better parameters than the current state of art (Alon, Panigrahy and Yekhanin, 2009). Our results further assert that polynomial (t ≥ nδ) data structure lower bounds against near-optimal space, would imply super-linear circuit lower bounds for log-depth linear circuits (a four-decade open question). In the succinct space regime (s = n + o(n)), we show that any improvement on current cell-probe lower bounds in the linear model would also imply new rigidity bounds. Our results rely on a new connection between the “inner" and “outer" dimensions of a matrix (Paturi and Pudlák, 2006), and on a new reduction from worst-case to average-case rigidity, which is of independent interest.

Original languageEnglish (US)
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Pages967-978
Number of pages12
ISBN (Electronic)9781450367059
DOIs
StatePublished - Jun 23 2019
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: Jun 23 2019Jun 26 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
CountryUnited States
CityPhoenix
Period6/23/196/26/19

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Circuit lower bound
  • Codes
  • Data structures
  • Rigidity

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