多项式时间对应于多项式长度的多项式常微分方程的解
Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
摘要：
我们提供了一个隐式表征的多项式时间计算的常微分方程：我们描述类$\operatorname{PTIME}$的语言计算在多项式时间的微分方程与多项式的右手边。这一结果给出了$\operatorname{PTIME}$的一个纯连续（时间和空间）的优美而简单的特征。这是第一次这样的类的特点是只使用常微分方程。我们的特征扩展到功能可计算的多项式时间在现实中的意义上的可计算分析。这扩展到多项式时间以上的确定性复杂度类。这可能会提供一个新的视角对经典的复杂性，通过提供一种方法来定义复杂性类，如$\operatorname{PTIME}$，在一个非常简单的方式，没有任何参考的概念（离散）机。这也可以提供通过常微分方程来陈述关于计算复杂性的经典问题的方法，即~运用分析框架。
英文摘要：
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous (time and space) elegant and simple characterization of $\operatorname{PTIME}$. This is the first time such classes are characterized using only ordinary differential equations. Our characterization extends to functions computable in polynomial time over the reals in the sense of computable analysis. This extends to deterministic complexity classes above polynomial time. This may provide a new perspective on classical complexity, by giving a way to define complexity classes, like $\operatorname{PTIME}$, in a very simple way, without any reference to a notion of (discrete) machine. This may also provide ways to state classical questions about computational complexity via ordinary differential equations, i.e.~by using the framework of analysis.
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