I'm interested in the computational power of neural nets. It is generally accepted that recurrent neural nets are Turing complete. Now I was searching for some papers which proofs this.

What I found so far:

• Turing computability with neural nets, Hava T. Siegelmann and Eduardo D. Sontag, 1991

  I think this is only interesting from a theoretical point of view because it needs to have the neuron activity of infinite exactness (to encode the state somehow as a rational number).

• S. Franklin and M. Garzon, Neural computability

  This needs an unbounded number of neurons and also doesn't really seem to be that much practical.

(Note that another question of mine tries to point out this kind of problem between such theoretical results and the practice.)

I'm searching mostly for some neural net which really can execute some code which I can also simulate and test in practice. Of course, in practice, they would have some kind of limited memory.

Does anyone know something like this?