## 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, except for the first layer. For every width d and length n, our pseudorandom generator uses a seed of length O((log d + loglogn + log(1) 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. 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 nonregular) branching program of length n and width d has the property that every vertex in the program is traversed with probability at least ? on a uniformly random input, then the error of the generator above is at most 2/λ^{2}. Finally, we show that the set of all binary strings with less than d nonzero entries forms a hitting set for regular width d branching programs.

Original language | English (US) |
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Pages (from-to) | 973-986 |

Number of pages | 14 |

Journal | SIAM Journal on Computing |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - 2014 |

## All Science Journal Classification (ASJC) codes

- General Computer Science
- General Mathematics

## Keywords

- Bounded space computation
- Branching programs
- Pseudorandom generators