Sequences of state configurations realizable by the network of a single threshold element

Abstract

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.

On the Sequence of State Configurations in the Garden of Eden

“…Autonomous threshold element circuit networks are gaining increased attention as a logical model for neural networks, and corresponding studies regarding the operation of such networks are therefore also increasing [1]. Furthermore, numerous studies have focused on the structure of the sequences of state configurations to investigate the operation of circuit networks [2][3][4][5][6][7][8]. Majority of these studies performed logical analysis in relation to structural elements in circuit networks, and the clarified nature of the elements often only has local validity in relation to the circuit networks.…”