## Abstract

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 = {g_{n} : {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 g_{n}(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 g_{n}^{-1}(1). The algorithm makes (2^{w}/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 language | English |
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Pages (from-to) | 1557-1570 |

Number of pages | 14 |

Journal | SIAM Journal on Computing |

Volume | 31 |

Issue number | 5 |

DOIs | |

State | Published - May 2002 |

## Keywords

- Branching programs
- Property testing
- Randomized algorithms

## ASJC Scopus subject areas

- Computer Science (all)
- Mathematics (all)