The main themes: approximate decision and sublinear complexity -- Testing linearity (group homomorphism) -- Low-degree tests -- Testing monotonicity -- Testing dictatorships, juntas, and monomials -- Testing by implicit sampling -- Lower bounds techniques -- Testing graph properties in the dense graph model -- Testing graph properties in the bounded-degree graph models -- Testing graph properties in the general graph model -- Testing properties of distributions -- Ramifications and related topics -- Locally testable codes and proofs.
0
SUMMARY OR ABSTRACT
Text of Note
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.