Contrary to the recent top comment on this, which fails to show that such a net existing could be no coincidence, I guess, the answer to your problem might be d

Contrary to the recent top comment on this, which fails to show that such a net existing could be no coincidence, I guess, the answer to your problem might be deeply physical and information theoretic, as soon as you speak of time. Simply speaking, any model is good enough if the approximation is tolerably accurate. In that sense, crude nets as well as expert systems that trigger off clear signals and ample evidence may already exist. In particular, the way the stockmarkets are distributed the function of time is likely relativistic and every participant is acting under incomplete information even in the infinite limit. Also, you have to be cautious what any function in this context really means, as I imagine it means differentiable functions (after somebody mentioned the Ackermann function, which is not anywhere differentiable).