Hierarchy theorems for property testing

Oded Goldreich; Michael Krivelevich; Ilan Newman; Eyal Rozenberg

doi:10.1007/978-3-642-03685-9_38

Hierarchy theorems for property testing

Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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, 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.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings
Pages	504-519
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-642-03685-9_38
State	Published - 2009
Event	12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009 - Berkeley, CA, United States Duration: 21 Aug 2009 → 23 Aug 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5687 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009
Country/Territory	United States
City	Berkeley, CA
Period	21/08/09 → 23/08/09

Keywords

Adaptivity vs non-adaptivity
Graph blow-up
Graph properties
Monotone graph properties
One-sided vs two-sided error
Property testing

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

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

Cite this

Goldreich, O., Krivelevich, M., Newman, I., & Rozenberg, E. (2009). Hierarchy theorems for property testing. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings (pp. 504-519). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5687 LNCS). https://doi.org/10.1007/978-3-642-03685-9_38

Goldreich, Oded ; Krivelevich, Michael ; Newman, Ilan et al. / Hierarchy theorems for property testing. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings. 2009. pp. 504-519 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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, 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.",

keywords = "Adaptivity vs non-adaptivity, Graph blow-up, Graph properties, Monotone graph properties, One-sided vs two-sided error, Property testing",

author = "Oded Goldreich and Michael Krivelevich and Ilan Newman and Eyal Rozenberg",

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Goldreich, O, Krivelevich, M, Newman, I & Rozenberg, E 2009, Hierarchy theorems for property testing. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5687 LNCS, pp. 504-519, 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009, Berkeley, CA, United States, 21/08/09. https://doi.org/10.1007/978-3-642-03685-9_38

Hierarchy theorems for property testing. / Goldreich, Oded; Krivelevich, Michael; Newman, Ilan et al.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings. 2009. p. 504-519 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5687 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Krivelevich, Michael

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AU - Rozenberg, Eyal

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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.

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Goldreich O, Krivelevich M, Newman I, Rozenberg E. Hierarchy theorems for property testing. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings. 2009. p. 504-519. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-03685-9_38

Hierarchy theorems for property testing

Abstract

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Keywords

ASJC Scopus subject areas

Access to Document

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