Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer

@article{Bournez2013TuringMC,
title={Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer},
author={O. Bournez and D. S. Graça and A. Pouly},
journal={ArXiv},
year={2013},
volume={abs/1203.4667}
}

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some… CONTINUE READING