Lower bounds for adaptive linearity tests

Linearity tests are randomized algorithms which have oracle access to the truth table of some function f, and are supposed to distinguish between linear functions and functions which are far from linear. Linearity tests were first introduced by Blum, Luby and Rubenfeld in [BLR93], and were later used in the PCP theorem, among other applications. The quality of a linearity test is described by its correctness c - the probability it accepts linear functions, its soundness s - the probability it accepts functions far from linear, and its query complexity q - the number of queries it makes. Linearity tests were studied in order to decrease the soundness of linearity tests, while keeping the query complexity small (for one reason, to improve PCP constructions). Samorodnitsky and Trevisan constructed in [ST00] the Complete Graph Test, and prove that no Hyper Graph Test can perform better than the Complete Graph Test. Later in [ST06] they prove, among other results, that no non-adaptive linea...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Shachar Lovett
• Keywords: Complete Graph Test, CORR 2008, Education, Linear Functions, Linearity Tests