## Abstract

We present algorithms for testing if a (0,1)-matrix M has Boolean/binary rank at most d, or is ϵ-far from having Boolean/binary rank at most d (i.e., at least an ϵ-fraction of the entries in M must be modified so that it has rank at most d). For the Boolean rank we present a non-adaptive testing algorithm whose query complexity is O(d^{4}/ ϵ^{6}). For the binary rank we present a non-adaptive testing algorithm whose query complexity is O(2^{2d}/ϵ^{2}), and an adaptive testing algorithm whose query complexity is O(2^{2d}/ϵ). All algorithms are 1-sided error algorithms that always accept M if it has Boolean/binary rank at most d, and reject with probability at least 2/3 if M is ϵ-far from having Boolean/binary rank at most d.

Original language | English |
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Pages (from-to) | 1193-1210 |

Number of pages | 18 |

Journal | Theory of Computing Systems |

Volume | 65 |

Issue number | 8 |

DOIs | |

State | Published - Nov 2021 |

## Keywords

- Binary rank
- Boolean rank
- Property testing