On Autonomous Logic Nets of Threshold Elements

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 2kn (-<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 Manuscript received October 26, 1966; revised August 2, 1967, November 10, 1967, and December 19, 1967. S. Yajima was with the Dept. of Electronics, and is now with the Dept. of Elec. Engrg. II, Kyoto University, Kyoto, Japan. T. Ibaraki was with the Dept. of Electronics, Kyoto University, Kyoto, Japan. He is now with the Dept. of Computer Science, University of Illinois. Urbana, Ill. I. Kawano was with the Dept. of Electronics, Kyoto University, Kyoto, Japan. Hle is now with Hitachi Ltd., Yokohama, Japan. 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.