TY - JOUR
T1 - Hierarchy Theorems for Property Testing
AU - Goldreich, Oded
AU - Krivelevich, Michael
AU - Newman, Ilan
AU - Rozenberg, Eyal
N1 - Funding Information:
An extended abstract of this work appeared in the proceedings of RANDOM’09. Oded Goldreich was partially supported by an Israel Science Foundation grant (No. 1041/08). Michael Krivele-vich was partially supported by an Israel Science Foundation grant No. 1063/08, an USA-Israel BSF grant (No. 2006322), and a Pazy Memorial Award. Ilan Newman was partially supported by an Israel Science Foundation grant (No. 1011/06).
PY - 2012/3
Y1 - 2012/3
N2 - 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.
AB - 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.
KW - Property testing
KW - adaptivity versus non-adaptivity
KW - graph blow-up
KW - graph properties
KW - hierarchy theorems
KW - monotone graph properties
KW - one-sided versus two-sided error
KW - query complexity
UR - http://www.scopus.com/inward/record.url?scp=84859100910&partnerID=8YFLogxK
U2 - 10.1007/s00037-011-0022-4
DO - 10.1007/s00037-011-0022-4
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AN - SCOPUS:84859100910
SN - 1016-3328
VL - 21
SP - 129
EP - 192
JO - Computational Complexity
JF - Computational Complexity
IS - 1
ER -