Abstract
AbstractWe 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 two‐sided ϵ‐testing algorithm must query at least Ω(nδ) many queries for some fixed ϵ and δ. This shows that Newman's result [Testing of functions that have small width branching programs, SIAM J Comput 31 (2002), 1557–1570] cannot be generalized to read‐k‐times functions for k > 1. In addition, we exhibit a property that has also a representation by a CNF formula of constant clause size. Hence, the nontestability results extend to properties that in addition have small (constant size) 0‐witnesses. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004
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