Computation Beyond the Turing Limit

@article{Siegelmann1995ComputationBT,
  title={Computation Beyond the Turing Limit},
  author={Hava T. Siegelmann},
  journal={Science},
  year={1995},
  volume={268},
  pages={545 - 548}
}
Extensive efforts have been made to prove the Church-Turing thesis, which suggests that all realizable dynamical and physical systems cannot be more powerful than classical models of computation. A simply described but highly chaotic dynamical system called the analog shift map is presented here, which has computational power beyond the Turing limit (super-Turing); it computes exactly like neural networks and analog machines. This dynamical system is conjectured to describe natural physical… 

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