Extractors and lower bounds for locally samplable sources

Anindya De, Thomas Watson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We consider the problem of extracting randomness from sources that are efficiently samplable, in the sense that each output bit of the sampler only depends on some small number d of the random input bits. As our main result, we construct a deterministic extractor that, given any d-local source with min-entropy k on n bits, extracts Ω(k 2/nd) bits that are 2 -nΩ(1) -close to uniform, provided d ≤ o(log n) and k ≥ n 2/3+γ (for arbitrarily small constants γ > 0). Using our result, we also improve a result of Viola [2010] who proved a 1/2-O(1/ log n) statistical distance lower bound for o(log n)-local samplers trying to sample input-output pairs of an explicit boolean function, assuming the samplers use at most n+ n 1-δ random bits for some constant δ > 0. Using a different function, we simultaneously improve the lower bound to 1/2 - 2 -nΩ(1) and eliminate the restriction on the number of random bits.

Original languageEnglish (US)
Article number3
JournalACM Transactions on Computation Theory
Issue number1
StatePublished - Mar 2012


  • Extractors
  • Locally samplable sources
  • Lower bounds

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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