ANNs can simulate Turing machines and vice versa.

• A recurrent neural network (RNN) with unbounded precision and unbounded time can emulate a Turing machine step-for-step; discrete feedforward networks with sufficient depth and size can simulate arbitrary Boolean circuits and thus any computable function given enough resources.
• Conversely, a Turing machine can simulate any finite neural network by treating weights, activations and connectivity as data on its tape.