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computational complexity

, Volume 21, Issue 1, pp 129–192 | Cite as

Hierarchy Theorems for Property Testing

  • Oded GoldreichEmail author
  • Michael Krivelevich
  • Ilan Newman
  • Eyal Rozenberg
Article

Abstract

Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q). Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree graphs. While in two cases, the proofs are quite straightforward, and the techniques employed in the case of the dense graph model seem significantly more involved. Specifically, problems that arise and are treated in the latter case include (1) the preservation of distances between graph under a blow-up operation and (2) the construction of monotone graph properties that have local structure.

Keywords

Property testing hierarchy theorems query complexity graph properties monotone graph properties graph blow-up one-sided versus two-sided error adaptivity versus non-adaptivity 

Subject classification

68Q15 68W20 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Oded Goldreich
    • 1
    Email author
  • Michael Krivelevich
    • 2
  • Ilan Newman
    • 3
  • Eyal Rozenberg
    • 4
  1. 1.Department of Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Department of Computer ScienceHaifa UniversityHaifaIsrael
  4. 4.Department of Computer ScienceTechnionHaifaIsrael

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