On Autonomous Logic Nets of Threshold Elements

Abstract—A model of autonomous logic nets composed of n threshold elements is presented and several properties of a single threshold element are generalized to this model. The number of these nets is shown to be 2^kn³(½≤k≤l) for completely specified machines. The capacity of the net is defined and conjectured to be 2, similar to the case of a single threshold element. P and NPN classifications of the machines are proposed and applied to the enumeration of all periodic sequences of length 2ⁿ(n≤4) realizable by this net. The state assignment problem of the net is also treated. The existence of transition diagrams which cannot be realized by this model for any state assignment, or of those that can be realized for any state assignment, is shown, and it turns out that almost all completely specified machines belong to the former class when n is sufficiently large. Considering the synthesis of a net, an application of learning procedure is also discussed and it is pointed out that only periodic sequences of length 2" can be learned automatically.