Section 1.1 provides a very brief introduction to property testing, sketching its basic definition and providing an overview of its flavor and potential benefits. The pace here is fast and sketchy, unlike that in the rest of this chapter. The technical material is presented in Sections 1.2 and 1.3, which constitutes the main part of this chapter. A more detailed account of the organization of this part is provided in Section 1.1.4.

Everyone talks of big data. Of course, the issue is making good use of large amounts of data, which requires analyzing it. But such an analysis may mean various things. At one extreme, it may mean locating tiny and possibly rare (but valuable) pieces of information. At the other extreme, it may means detecting global structures or estimating global parameters of the data as a whole.

It is the latter meaning that applies to the field of property testing. This field is concerned with the analysis of global features of the data, such as determining whether the data as a whole have some global property or estimating some global parameter of their structure. The focus is on properties and parameters that go beyond simple statistics that refer to the frequency of the occurrence of various local patterns. This is not to suggest that such simple statistics are not of value, but rather that not everything of interest can be reduced to them.

In general, the data are a set of records (or items) that may be interrelated in various ways. The contents and meaning of the data may be reflected not only in the individual items (or records), but also in the relations between them.