Property Testing of the Boolean and Binary Rank

Michal Parnas*, Dana Ron, Adi Shraibman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present algorithms for testing if a (0,1)-matrix M has Boolean/binary rank at most d, or is ϵ-far from having Boolean/binary rank at most d (i.e., at least an ϵ-fraction of the entries in M must be modified so that it has rank at most d). For the Boolean rank we present a non-adaptive testing algorithm whose query complexity is O(d4/ ϵ6). For the binary rank we present a non-adaptive testing algorithm whose query complexity is O(22d2), and an adaptive testing algorithm whose query complexity is O(22d/ϵ). All algorithms are 1-sided error algorithms that always accept M if it has Boolean/binary rank at most d, and reject with probability at least 2/3 if M is ϵ-far from having Boolean/binary rank at most d.

Original languageEnglish
Pages (from-to)1193-1210
Number of pages18
JournalTheory of Computing Systems
Volume65
Issue number8
DOIs
StatePublished - Nov 2021

Keywords

  • Binary rank
  • Boolean rank
  • Property testing

Fingerprint

Dive into the research topics of 'Property Testing of the Boolean and Binary Rank'. Together they form a unique fingerprint.

Cite this