Property Testing and Communication Complexity

Suppose that we are given as input an object O and we’d like to know if it has some property P . But querying the object is expensive, so we would like to do a small number of local queries on the object. Usually, deciding with certainty whether an object has a property or not will require a lot of queries. The idea of property testing is to answer an easier question, thus allowing less queries to be made. In property testing, given the object O, the tester has to distinguish in between objects that satisfy the property P and objects that are far from the property. The notion of “being far” depends on what the object is (distribution, function, graph...). The tester’s efficiency is measured by the number of queries it does on the object.