Hierarchy theorems for property testing

Oded Goldreich*, Michael Krivelevich, Ilan Newman, Eyal Rozenberg

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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, 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 graphs under a blow-up operation, and (2) the construction of monotone graph properties that have local structure.

Original languageEnglish
Title of host publicationProperty Testing - Current Research and Surveys
Number of pages6
StatePublished - 2010
EventMini-Workshop on Property Testing - Beijing, China
Duration: 8 Jan 201010 Jan 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6390 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceMini-Workshop on Property Testing


  • Adaptivity versus Non-adaptivity
  • Graph Blow-up
  • Graph Properties
  • Monotone Graph Properties
  • One-Sided versus Two-Sided Error


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