Realization of Sequential Machines with Threshold Elements

The state assignment problem for finite-state sequential machines is examined in the context of threshold logic. An algorithm is developed for assigning binary codes to the states, inputs, and outputs so that the state variable and output variable functions satisfy the necessary condition of 2-assumability that they be linearly separable. The algorithm deals with 2-block partitions by which the assignments are made. First those partitions which cannot be used are computed. For each of the remaining partitions, a list is compiled of those partitions of which one must be used if the given partition is used. Finally, a method is given for constructing the sets of partitions satisfying these constraints and having zero product. Code assignments made by these partition sets will induce 2-asummable functions.