Ramifications and related topics

In some setting objects that are close to having the property may be almost as good for these settings as objects that have the property (e.g., see some of the settings discussed in Section [intro:benefits]). But in such a case, when testing for the property, it may be desirable not to reject objects that are very close to having the property (or, put differently, “tolerate” a small deviation). This leads to a natural generalization of the testing task that calls for distinguishing between objects that are ǫ′-close to the property and objects that are ǫ-far from the property, for parameters ǫ′ < ǫ. Indeed, standard property testing refers to the case of ǫ′ = 0, and tolerant testing may be viewed as “tolerating” a small deviation of the object from having the property, where typically ǫ′ is a function of ǫ (and sometimes also of n).