Algebraic reduction procedures for multivalued logic functions based upon a principally binary circuit realization are presented. The procedures given are also applicable to literal gate realizations employing compound literals. The prime implicant generation and covering problems are treated in detail. It is shown that the selected cover must be iteratively examined for possible reduction at each decision point of the covering process. This reduction is achieved by the elimination of unnecessary nonadjacencies.

Methods are presented for designing fault-detection experiments for sequential machines which are realized as parallel connections of simpler component machines. The outputs of these components are assumed to be inaccessible for measurement but it is shown that knowledge of the structure can be utilized to design simpler experiments. The procedure is based upon placing all components but one in a fixed reference state prior to measuring input/output sequences for this one component in order to deduce its state table. This means that the only measurable transitions are those which return the other components to their reference states. Such transitions are made in response to application of restricted input sequences and it is necessary that the state table be deduced from such a set of observations.

In this paper we present algorithms for designing fault-detection experiments for sequential machines with special emphasis on the case in which the machine does not possess a distinguishing sequence. The length of an experiment is reduced through: 1) identifying each state with its own unique input/output set rather than using a common set for all states; 2) utilizing overlapping of the required input/output sequences so that a portion of the experiment serves more than one purpose; and 3) verifying the reference condition in which the machine is placed at many points in the experiment by as short a locating sequence as possible. Important distinctions are made between locating sequences of the type introduced in previous work and those defined and used here.