SUMMARYThis paper presents a generation procedure for highorder threshold functions, considering the high-order neighbor vector and the monotonic property. Specifically, it is first shown that the high-order neighbor vector can be derived from an input vector which is noncomparable by the high-order threshold function. Then, it is shown that a monotonic function of a high-order variable can easily be generated from the given monotonic function. Based on the generation process for the monotonic function, the generation procedure for high-order threshold functions is derived. It is also shown that if a given high-order threshold function preserves monotonicity, the generated high-order threshold function also preserves monotonicity, and also the high-order terms.

The autonomous network composed of a threshold element and n delay elements can be considered as a logical model for the neural network. The discussion of the structure of the state configuration sequences, which are realizable by such a network, will give a clue to the logical operation of the neural network. This paper discusses the state configuration sequences realizable by such a network and the property of the threshold function using the connecting edges and boundary vectors. It is shown first that when the state configuration sequences can only be periodic, the maximum realizable length of the periodic sequences is 2n. Then the self-dual state configuration sequences are generated from the foregoing state configuration sequences, preserving a certain periodic sequence. It is shown that the network function in this case can be composed of an MBS function, and all boundary vectors and weights and thresholdscaneasily be determined. The structure of the realizable transient sequences is also discussed.