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 two-sided ε-testing algorithm must query at least Ω(n δ) 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.
|Number of pages||19|
|Journal||Random Structures and Algorithms|
|State||Published - Mar 2004|
ASJC Scopus subject areas
- Mathematics (all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics