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

Eldar Fischer, Ilan Newman, Jiří Sgall

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)175-193
Number of pages19
JournalRandom Structures and Algorithms
Volume24
Issue number2
DOIs
StatePublished - Mar 2004

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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