### Abstract

A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism ^{fσ} of f, we can compute ^{fσ}(x) for any xZ2n with good probability using q queries to g. We observe that any k-junta, that is, any function which depends only on k of its input variables, is O(2 ^{k})-locally correctable. Moreover, we show that there are examples where this is essentially best possible, and locally correcting some k-juntas requires a number of queries which is exponential in k. These examples, however, are far from being typical, and indeed we prove that for almost every k-junta, O(klogk) queries suffice.

Original language | English (US) |
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Pages (from-to) | 223-226 |

Number of pages | 4 |

Journal | Information Processing Letters |

Volume | 112 |

Issue number | 6 |

DOIs | |

State | Published - Mar 15 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

### Keywords

- Local correction
- Locally correctable codes
- Randomized algorithms

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## Cite this

*Information Processing Letters*,

*112*(6), 223-226. https://doi.org/10.1016/j.ipl.2011.12.005