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 I similar to(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.
Original languageEnglish
Pages (from-to)129-192
Number of pages64
JournalComputational Complexity
Issue number1
StatePublished - Mar 2012


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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Computational Mathematics


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