# Property testing and its connection to learning and approximation

@article{Goldreich1996PropertyTA, title={Property testing and its connection to learning and approximation}, author={Oded Goldreich and Shafi Goldwasser and Dana Ron}, journal={Proceedings of 37th Conference on Foundations of Computer Science}, year={1996}, pages={339-348} }

The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between property testing and problems in learning theory. Next, they focus on testing graph properties, and…

## 919 Citations

### Property Testing: A Learning Theory Perspective

- MathematicsCOLT
- 2007

Property testing [15,9] is the study of the following class of problems: Given the ability to perform local queries concerning a particular object, the problem is to determine whether the object has a predetermined global property, or differs significantly from any object that has the property.

### Property Testing

- Computer ScienceAlgorithms for Big Data
- 2020

Property Testing: A Learning Theory Perspective takes the learning-theory point of view of property testing and focuses on results for testing properties of functions that are of interest to the learning theory community, including algebraic properties, which include testing whether a function is (multi-)linear and more generally whether it is a polynomial of bounded degree.

### Testing versus estimation of graph properties

- Computer Science, MathematicsSTOC '05
- 2005

It is shown here that in the setting of the dense graph model, all testable properties are not only tolerantly testable, but also admit a constant query size algorithm that estimates the distance from the property up to any fixed additive constant.

### Combinatorial property testing (a survey)

- MathematicsRandomization Methods in Algorithm Design
- 1997

This work considers the question of determining whether a given object has a predetermined property or is \far" from any object having the property, and focuses on combinatorial properties, and speciically on graph properties.

### Three theorems regarding testing graph properties

- Mathematics, Computer ScienceProceedings 2001 IEEE International Conference on Cluster Computing
- 2001

Three theorems regarding testing graph properties in the adjacency matrix representation are presented and every graph property that can be tested making a number of queries that is independent of the size of the graph, can be so tested by uniformly selecting a set of vertices.

### Algorithmic and Analysis Techniques in Property Testing

- Computer Science, MathematicsFound. Trends Theor. Comput. Sci.
- 2009

This monograph surveys results in property testing, where the emphasis is on common analysis and algorithmic techniques.

### Active Property Testing

- Computer Science2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

A general notion of the testing dimension of a given property with respect to a given distribution is developed, that characterizes (up to constant factors) the intrinsic number of label requests needed to test that property.

### The Classi cation Problem in Relational Property Testing

- Computer Science
- 2009

This thesis introduces a generalization of property testing which is inspired by the classical problem for decidability and considers the testability of various syntactic fragments of rst-order logic.

### Testing Eulerianity and connectivity in directed sparse graphs

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2011

### On the Testability of Graph Partition Properties

- Computer Science, MathematicsAPPROX-RANDOM
- 2018

This work studies the testability of a family of graph partition properties that generalizes a family previously studied by Goldreich, Goldwasser, and Ron and shows that every property in GPP is testable by a one-sided error algorithm that has query complexity poly(1/ ) and that if P ∈ GPP\GPP0,1 then it cannot have aOne- sided error testing algorithm whose query complexity is independent of the input graph's size.

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