A linear algorithm for the merli scan is described which exhibits a better quantization SNR than a nonlinear algorithm proposed by Limb and is more easily implemented. The error propagation characteristics for the linear algorithm are similar to those for the Limb algorithm.

The least upper bound of n(n−1)/2 input symbols is derived for the total length of characterizing sequences for a reduced n-state machine. When a machine can be characterized by a set of r characterizing sequences, a reduced upper bound on their total length will be r(2n−r−1)/2 input symbols. To shorten transfer sequences, better use is made of the strong-connectedness assumptions of the machines to be tested. The reduced bounds on characterizing and transfer sequences are utilized to improve the upper bounds on checking experiments employing simple input/output (I/O) sequences.

The problem treated in this paper is that of realizing a Boolean function which is not linearly separable with a network of threshold gates. This problem has been treated by the tree method of Coates and Lewis [1], the geometric methods of Winder [5], and the algebraic methods of Hopcroft and Mattson [3] and Stabler [4] among others. In the above methods, the techniques become computationally impractical for a large number of variables and functions requiring several threshold gates. The method presented in this paper suffers from the same limitations, as well as from the fact that it is based entirely on necessary but not sufficient conditions for linear separability.