  We present algorithms for testing if a $(0,1)$-matrix $M$ has Boolean/binary
rank at most $d$, or is $\epsilon$-far from Boolean/binary rank $d$ (i.e., at
least an $\epsilon$-fraction of the entries in $M$ must be modified so that it
has rank at most $d$).
  The query complexity of our testing algorithm for the Boolean rank is
$\tilde{O}\left(d^4/ \epsilon^6\right)$. For the binary rank we present a
testing algorithm whose query complexity is $O(2^{2d}/\epsilon)$.
  Both 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 $\epsilon$-far from Boolean/binary rank $d$.
