## Abstract

Combinatorial property testing, initiated formally by Goldreich, Goldwasser and Ron in [11], and inspired by Rubinfeld and Sudan, 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 being `far' from having the property. The main result here is that if G = {g : {0,1}^{n}→{0, 1}} is a family of Boolean functions that have 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(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^{-1} (1). The algorithm queries (2^{w}/ε)^{O(w)} many queries. In particular, for constant ε and w, the query complexity is O(1). This generalizes the results of Alon et. al. asserting that regular languages are efficiently (ε, O(1))-testable.

Original language | English |
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Pages (from-to) | 251-257 |

Number of pages | 7 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

State | Published - 2000 |

Event | 41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA Duration: 12 Nov 2000 → 14 Nov 2000 |

## ASJC Scopus subject areas

- Hardware and Architecture