论文标题
资源共享机的代数
An Algebra of Resource Sharing Machines
论文作者
论文摘要
动态系统是用于描述物理和计算过程演变的广泛数学工具。传统上，这些过程模拟了静态世界中改变实体。想象一个在空桌子上滚动的球。相反，开放的动力系统模型在不断变化的世界中改变实体。在正在进行的台球比赛中拍摄球。在文献中，关于开放动力学系统中“开放”的解释存在歧义。换句话说，开放动态系统相互作用的机制存在歧义。在某些方面，开放的动力系统是输入输出机，它们通过将一个系统的输入与另一个系统的输出相互作用。对于其他人来说，开放的动态系统是输入输出不可知论，并通过共享的资源池进行交互。在本文中，我们定义了开放动力学系统的代数，该系统统一了这两个观点。我们详细考虑了动态系统的两个具体实例 - 在歧管和非确定性自动机上连续流。
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty table. In contrast, open dynamical systems model changing entities in a changing world. Picture a ball in an ongoing game of billiards. In the literature, there is ambiguity about the interpretation of the "open" in open dynamical systems. In other words, there is ambiguity in the mechanism by which open dynamical systems interact. To some, open dynamical systems are input-output machines which interact by feeding the input of one system with the output of another. To others, open dynamical systems are input-output agnostic and interact through a shared pool of resources. In this paper, we define an algebra of open dynamical systems which unifies these two perspectives. We consider in detail two concrete instances of dynamical systems -- continuous flows on manifolds and non-deterministic automata.
