TY - GEN

T1 - Hierarchy theorems for property testing

AU - Goldreich, Oded

AU - Krivelevich, Michael

AU - Newman, Ilan

AU - Rozenberg, Eyal

PY - 2009

Y1 - 2009

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 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, 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 - Adaptivity vs non-adaptivity

KW - Graph blow-up

KW - Graph properties

KW - Monotone graph properties

KW - One-sided vs two-sided error

KW - Property testing

UR - http://www.scopus.com/inward/record.url?scp=70449717879&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03685-9_38

DO - 10.1007/978-3-642-03685-9_38

M3 - Conference contribution

AN - SCOPUS:70449717879

SN - 3642036848

SN - 9783642036842

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

SP - 504

EP - 519

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009

Y2 - 21 August 2009 through 23 August 2009

ER -