AbstractÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset g of points in an undirected graph q Y i is called an identifying code if the sets fv g consisting of all elements of g within distance one from the vertex v are different. We also require that the sets fv g are all nonempty. We take q to be the infinite square lattice with diagonals and show that the density of the smallest identifying code is at least 2/9 and at most 4/17.