On the computational capability of recurrent higher‐order neural networks
Ken Tanaka, Daigo Hasegawa · Systems and Computers in Japan · 2001
Abstract A neural network composed of a finite number of continuous value output neurons is known to be able to simulate any deterministic Turing machine. Several simulation models have been proposed, but there remains the problem that a massive number of neurons is needed to simulate the tape part in real time. In this paper the authors demonstrate that a recurrent higher‐order neural network can simulate any Turing machine, then specify the lower limit for the number of neurons required and the time needed for the simulation. First, the authors show that a recurrent higher‐order neural network consisting of a limited number of neurons using a threshold input/output function and a linear input/output function can simulate any deterministic Turing machine in real time, and that the number of neurons required to simulate the tape can be reduced to six. Then the authors show that if a saw‐type function is used, the number of neurons required for the simulation can be reduced to four. A simplified simulation model is then offered as a viable framework for learning formal language using a neural network. © 2001 Scripta Technica, Syst Comp Jpn, 32(10): 42–50, 2001