Property Testing of the Boolean and Binary Rank

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 Õ (d^4/ ϵ ^6 ) . For the binary rank we present a non-adaptive testing algorithm whose query complexity is O (2 2 d / 𝜖 2 ), and an adaptive testing algorithm whose query complexity is O (2 2 d / 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 .