TY - GEN

T1 - Hierarchy theorems for property testing

AU - Goldreich, Oded

AU - Krivelevich, Michael

AU - Newman, Ilan

AU - Rozenberg, Eyal

PY - 2010

Y1 - 2010

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, 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.

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, 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.

KW - Adaptivity versus Non-adaptivity

KW - Graph Blow-up

KW - Graph Properties

KW - Monotone Graph Properties

KW - One-Sided versus Two-Sided Error

UR - http://www.scopus.com/inward/record.url?scp=78449296060&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-16367-8_22

DO - 10.1007/978-3-642-16367-8_22

M3 - Conference contribution

AN - SCOPUS:78449296060

SN - 3642163661

SN - 9783642163661

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 289

EP - 294

BT - Property Testing - Current Research and Surveys

T2 - Mini-Workshop on Property Testing

Y2 - 8 January 2010 through 10 January 2010

ER -