Proximity oblivious testing and the role of invariances

Oded Goldreich, Tali Kaufman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

5 Scopus citations


We present a general notion of properties that are characterized by local conditions that are invariant under a sufficiently rich class of symmetries. Our framework generalizes two popular models of testing graph properties as well as the algebraic invariances studied by Kaufman and Sudan (STOC'08). Our focus is on the case that the property is characterized by a constant number of local conditions and a rich set of invariances. We show that, in the aforementioned models of testing graph properties, characterization by such invariant local conditions is closely related to proximity oblivious testing (as defined by Goldreich and Ron, STOC'09). In contrast to this relation, we show that, in general, characterization by invariant local conditions is neither necessary nor sufficient for proximity oblivious testing. Furthermore, we show that easy testability is not guaranteed even when the property is characterized by local conditions that are invariant under a 1-transitive group of permutations.

Original languageEnglish
Title of host publicationStudies in Complexity and Cryptography
Subtitle of host publicationMiscellanea on the Interplay between Randomness and Computation
EditorsOded Goldreich
Number of pages18
StatePublished - 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6650 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Graph Properties
  • Locally Testable Codes
  • Property Testing
  • Sparse Linear Codes
  • The Long-Code


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