This letter reports on the condition for applying a feedback connection to a deterministic finite automata. First we define the partial delayed dependence condition for the feedback connection, and then consider problems related to the completeness problem of automata.

This article deals with the binary neural network with negative self-feedback connections as a method for solving combinational optimization problems. Although the binary neural network has a high convergence speed, it hardly searches out the optimum solution, because the neuron is selected randomly at each state update. In thie article, an improvement using the negative self-feedback is proposed. First it is shown that the negative self-feedback can make some local minimums be unstable. Second a selection rule is proposed and its property is analyzed in detail. In the binary neural network with negative self-feedback, this selection rule is effective to escape a local minimum. In order to comfirm the effectiveness of this selection rule, some computer simulations are carried out for the N-Queens problem. For N=256, the network is not caught in any local minimum and provides the optimum solution within 2654 steps (about 10 minutes).