On the Sequence of State Configurations in the Garden of Eden
This work addresses a specific theoretical issue in neural network modeling using threshold circuits, but it appears incremental as it builds on known concepts like Garden of Eden sequences without claiming broad advances.
The study tackled the problem of identifying sequences of state configurations that cannot be transitioned in autonomous threshold element circuit networks, focusing on logical functions of four or fewer variables, and showed that using Garden of Eden sequences makes it easy to obtain functions for circuit network operation.
Autonomous threshold element circuit networks are used to investigate the structure of neural networks. With these circuits, as the transition functions are threshold functions, it is necessary to consider the existence of sequences of state configurations that cannot be transitioned. In this study, we focus on all logical functions of four or fewer variables, and we discuss the periodic sequences and transient series that transition from all sequences of state configurations. Furthermore, by using the sequences of state configurations in the Garden of Eden, we show that it is easy to obtain functions that determine the operation of circuit networks.