Property Testing via Set-Theoretic Operations

: Given two testable properties P1 and P2, under what conditions are the union, intersection or set-difference 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/ 2 ), where is the distance parameter.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Victor Chen, Madhu Sudan, Ning Xie
• Keywords: CORR 2010, Education, Query Complexity, Testable, Worse Query Complexity