Abstract|We consider the set of control points in a discrete device where testing is organized
in groups with a signature analyzer. We solve the localization problem for a fault of any
multiplicity located in one or different groups. For this purpose, in addition we construct
various partitions of the set of control points where we organize similar group testing. We show
an algorithm for constructing additional partitions. We solve the minimization problem for the
testing hardware needed to implement it.