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 \(\tilde {O}\left (d^{4}/ \epsilon ^{6}\right )\). For the binary rank we present a non-adaptive testing algorithm whose query complexity is O(2^2d/𝜖²), 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.

我们提出了用于测试 (0,1)-矩阵M是否具有最多d 的布尔/二进制秩的算法，或者是𝜖 - 远不具有最多d 的布尔/二进制秩（即，至少有一个𝜖 - 条目的分数必须修改in M以使其具有最多d 的等级）。对于布尔等级，我们提出了一种非自适应测试算法，其查询复杂度为\(\tilde {O}\left (d^{4}/ \epsilon ^{6}\right )\)。对于二进制排名，我们提出了一种非自适应测试算法，其查询复杂度为O (2 ^{2 d} / 𝜖 ²)，以及查询复杂度为O (2 ^{2 d} / 𝜖 )的自适应测试算法。所有算法都是单边误差算法，如果M 的布尔/二进制秩最多为d，则总是接受M，如果M是𝜖，则以至少 2/3 的概率拒绝- 远不具有布尔/二进制秩最多d。