Open AccessBook
Introduction to Property Testing
TLDR
In this article, a wide range of algorithmic techniques for the design and analysis of tests for algebraic properties, properties of Boolean functions, graph properties, and properties of distributions are presented.Abstract:
Property testing is concerned with the design of super-fast algorithms for the structural analysis of large quantities of data. The aim is to unveil global features of the data, such as determining whether the data has a particular property or estimating global parameters. Remarkably, it is possible for decisions to be made by accessing only a small portion of the data. Property testing focuses on properties and parameters that go beyond simple statistics. This book provides an extensive and authoritative introduction to property testing. It provides a wide range of algorithmic techniques for the design and analysis of tests for algebraic properties, properties of Boolean functions, graph properties, and properties of distributions.read more
Citations
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Book ChapterDOI
The knowledge complexity of interactive proof-systems
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Journal Article
Property Testing and its connection to Learning and Approximation
TL;DR: In this paper, the authors consider the question of determining whether a function f has property P or is e-far from any function with property P. In some cases, it is also allowed to query f on instances of its choice.
Journal Article
Improved low-degree testing and its applications
Sanjeev Arora,Madhu Sudan +1 more
TL;DR: A new, and surprisingly strong, analysis is presented which shows that the preceding statement is true for arbitrarily small δ, provided the field size is polynomially larger than d/δ, and produces a self tester/corrector for any buggy program that computes a polynomial over a finite field.
Journal ArticleDOI
Linear Zero-Knowledgde. A Note on Efficient Zero-Knowledge Proofs and Arguments
Ivan Damgård,Ronald Cramer +1 more
TL;DR: Two protocols based on a Boolean formula Phi containing and- , or- and not-operators which verifies an NP-witness of membership in L have the smallest known asymptotic communication complexity among general proofs or arguments for NP.
Journal Article
Improved Testing Algorithms for Monotonicity.
TL;DR: Improved algorithms for testing monotonicity of functions are presented, given the ability to query an unknown function f: Σ n ↦ Ξ, and the test always accepts a monotone f, and rejects f with high probability if it is e-far from being monotones.
References
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Book
The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
Proceedings ArticleDOI
A theory of the learnable
TL;DR: This paper regards learning as the phenomenon of knowledge acquisition in the absence of explicit programming, and gives a precise methodology for studying this phenomenon from a computational viewpoint.
Book
Randomized Algorithms
TL;DR: This book introduces the basic concepts in the design and analysis of randomized algorithms and presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications.
Journal ArticleDOI
The knowledge complexity of interactive proof systems
TL;DR: A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.
Book
Approximation Algorithms for NP-Hard Problems
TL;DR: This book reviews the design techniques for approximation algorithms and the developments in this area since its inception about three decades ago and the "closeness" to optimum that is achievable in polynomial time.