  We consider the problem of deciding if a set of quantum one-qudit gates
$\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide the compact form
criteria leading to a simple algorithm that allows deciding universality of any
given set of gates in a finite number of steps. Moreover, for a non-universal
$\mathcal{S}$ our criteria indicate what type of gates can be added to
$\mathcal{S}$ to turn it into a universal set.
