Functions that have read-twice constant width branching programs are not necessarily testable

Abstract

We construct a property on 0/1-strings that has a representation by a collection of width 3, read-twice oblivious branching programs, but for which any 2-sided /spl epsi/-testing algorithm must make at least /spl Omega/(n/sup 1/10/) many queries for some fixed small enough /spl epsi/. This shows that Newman's result (2000) cannot be generalized to read-k-times functions for k > 1.