Property Testing via Set-Theoretic Operations

Given two testable properties P1 and P2, under what conditions are the union, intersection or setdifference of these two properties also testable? We initiate a systematic study of these basic set-theoretic operations in the context of property testing. As an application, we give a conceptually different proof that linearity is testable, albeit with much worse query complexity. Furthermore, for the problem of testing disjunction of linear functions, which was previously known to be one-sided testable with a super-polynomial query complexity, we give an improved analysis and show it has query complexity O(1/ǫ), where ǫ is the distance parameter. Princeton University. [email protected]. Microsoft Research New England. [email protected]. Research supported in part by NSF Award CCR-0514915. MIT CSAIL. [email protected]. Research supported in part by NSF Award CCR-0514771, 0728645 and 0732334.