Computing over the Reals: Foundations for Scientific Computing
<|reference_start|>Computing over the Reals: Foundations for Scientific Computing: We give a detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and argue that this is a good way to formalize many problems of scientific computation. In the introduction we also discuss the alternative Blum-Shub-Smale model. In the final section we discuss the issue of whether physical systems could defeat the Church-Turing Thesis.<|reference_end|>
@article{braverman2005computing,
    title={Computing over the Reals: Foundations for Scientific Computing},
    author={Mark Braverman, Stephen Cook},
    journal={arXiv preprint arXiv:cs/0509042},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0509042},
    primaryClass={cs.CC cs.LO}
}