property testing
relabelling
testability
results
conditions
knowledge
en
theorem
vector space
domain
samples
https://scigraph.springernature.com/explorer/license/
pieces
identification
space
fact
global properties
class of properties
211-227
broad conditions
local testability
recent results
algebraic properties
structural theorem
invariance
data
transformation
chapters
Property testing considers the task of testing rapidly (in particular, with very few samples into the data), if some massive data satisfies some given property, or is far from satisfying the property. For “global properties”, i.e., properties that really depend somewhat on every piece of the data, one could ask how it can be tested by so few samples? We suggest that for “natural” properties, this should happen because the property is invariant under “nice” set of “relabellings” of the data. We refer to this set of relabellings as the “invariance class” of the property and advocate explicit identification of the invariance class of locally testable properties. Our hope is the explicit knowledge of the invariance class may lead to more general, broader, results.After pointing out the invariance classes associated with some the basic classes of testable properties, we focus on “algebraic properties” which seem to be characterized by the fact that the properties are themselves vector spaces, while their domains are also vector spaces and the properties are invariant under affine transformations of the domain. We survey recent results (obtained with Tali Kaufman, Elena Grigorescu and Eli Ben-Sasson) that give broad conditions that are sufficient for local testability among this class of properties, and some structural theorems that attempt to describe which properties exhibit the sufficient conditions.
properties
satisfies
set
testing
sufficient conditions
hope
invariance classes
class
explicit knowledge
task
Invariance in Property Testing
chapter
task of testing
explicit identification
affine transformation
2010-01-01
testable properties
2010
basic classes
https://doi.org/10.1007/978-3-642-16367-8_12
data satisfies
true
2022-05-20T07:48
Goldreich
Oded
Microsoft Research New England, One Memorial Drive, 02142, Cambridge, MA, USA
Microsoft Research New England, One Memorial Drive, 02142, Cambridge, MA, USA
10.1007/978-3-642-16367-8_12
doi
Sudan
Madhu
dimensions_id
pub.1047100906
Mathematical Sciences
978-3-642-16367-8
Property Testing
978-3-642-16366-1
Springer Nature
Pure Mathematics
Springer Nature - SN SciGraph project