On Precision of Recurrent Higher-Order Neural Network that Simulates Turing Machines

Abstract

When a neural network simulates a Turing machine, the states of finite state controller and the symbols on infinite tape are encoded in continuous numbers of neuron's outputs. The precision of outputs is regarded as a space resource in neural computations. We show a sufficient condition about the precision to guarantee the correctness of computations. Linear precision suffice in regard to nT, where n is the number of neurons and T is the iteration count of state updates.