Testing membership in languages that have small width branching programs

Research output: Contribution to journalArticlepeer-review


Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653-750] and inspired by Rubinfeld and Sudan [SIAM J. Comput., 25 (1996), pp 252-271, deals with the following relaxation of decision problems: Given a fixed property and an input x, one wants to decide whether x has the property or is "far" from having the property. The main result here is that, if G = {gn : {0, 1}n → {0, 1}} is a family of Boolean functions which have oblivious read-once branching programs of width w, then, for every n and ε > 0, there is a randomized algorithm that always accepts every x ∈ {0, 1}n if gn(x) = 1 and rejects it with high probability if at least εn bits of x should be modified in order for it to be in gn-1(1). The algorithm makes (2w/ε)O(w)queries. In particular, for constant ε and w, the query complexity is O(1). This generalizes the results of Alon et al. [Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, 1999, pp. 645-655] asserting that regular languages are ε-testable for every ε > 0.

Original languageEnglish
Pages (from-to)1557-1570
Number of pages14
JournalSIAM Journal on Computing
Issue number5
StatePublished - May 2002


  • Branching programs
  • Property testing
  • Randomized algorithms

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


Dive into the research topics of 'Testing membership in languages that have small width branching programs'. Together they form a unique fingerprint.

Cite this