Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length

@article{Bournez2017PolynomialTC,
title={Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length},
author={O. Bournez and D. Graça and A. Pouly},
journal={Journal of the ACM (JACM)},
year={2017},
volume={64},
pages={1 - 76}
}

The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class P of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous elegant and simple characterization of P. We believe it is the first time complexity classes are characterized using only ordinary differential… CONTINUE READING