### Abstract

We give new pseudorandom generators for regular read-once branching programs of small width. A branching program is regular if the in-degree of every vertex in it is either 0 or 2. For every width d and length n, our pseudorandom generator uses a seed of length O((log d + log log n + log(1/ε)) log n) to produce n bits that cannot be distinguished from a uniformly random string by any regular width d length n read-once branching program, except with probability ε. We also give a result for general read-once branching programs, in the case that there are no vertices that are reached with small probability. We show that if a (possibly non-regular) branching program of length n and width d has the property that every vertex in the program is traversed with probability at least γ on a uniformly random input, then the error of the generator above is at most 2ε/γ ^{2}.

Original language | English (US) |
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Title of host publication | Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |

Pages | 40-47 |

Number of pages | 8 |

DOIs | |

State | Published - Dec 1 2010 |

Externally published | Yes |

Event | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, NV, United States Duration: Oct 23 2010 → Oct 26 2010 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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ISSN (Print) | 0272-5428 |

### Other

Other | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |
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Country | United States |

City | Las Vegas, NV |

Period | 10/23/10 → 10/26/10 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Keywords

- Branching programs
- Explicit constructions
- Pseudorandomness

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## Cite this

*Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010*(pp. 40-47). [5670950] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2010.11