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Hierarchy Theorems for Property Testing

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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.

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Authors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich

  2. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Michael Krivelevich

  3. Department of Computer Science, Haifa University, Haifa, Israel

    Ilan Newman

  4. Department of Computer Science, Technion, Haifa, Israel

    Eyal Rozenberg

Authors
  1. Oded Goldreich
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  2. Michael Krivelevich
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  3. Ilan Newman
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  4. Eyal Rozenberg
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Correspondence to Oded Goldreich.

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Goldreich, O., Krivelevich, M., Newman, I. et al. Hierarchy Theorems for Property Testing. comput. complex. 21, 129–192 (2012). https://doi.org/10.1007/s00037-011-0022-4

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  • DOI: https://doi.org/10.1007/s00037-011-0022-4

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