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 -