In this paper I elaborated on the idea of David Harel and Amir Pnueli to distinguish systems according to their compositional behavior. The basic idea is to assume a functional relation between state functions as the system-constituting property, allowing to partition the world into a system and a rest. The obvious idea to base the composition of systems on the concept of computable functions and their compositional behavior leads to supersystem formation by composing simple and recursive systems. But this approach does not allow to account adequately for systems that interact with many other systems in a stateful and nondeterministic way which is why I introduce the concept of interactivity and cooperation. In order to describe interactive systems satisfactorily, a balance is needed between the representation of their relationship to all the other systems and what happens within the systems. I thus introduce the complementary descriptions of external interactions and internal coordination, both based on a role concept in the sense of a projection of a system onto its interactions. Beside the interesting distinction between composition, cooperation and coordination, the presented approach also fits well with other rather well known concepts. First the concept of components and interfaces. Components become systems with a well defined compositional behavior were the interface concept captures both, the transformational and the compositional behavior of a system in its interactions. Another tightly related concept is that of decisions and games. I introduce the concept of decisions as an additional internal input alphabet in order to determine nondeterministic interactions and thus fictitiously assume a system function where we actually do not have the knowledge to do so. Thus, the close relationship between protocols and games becomes obvious.

中文翻译：

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计算系统的组成、合作和协调

在这篇论文中，我详细阐述了 David Harel 和 Amir Pnueli 根据系统的组成行为来区分系统的想法。基本思想是假设状态函数之间的函数关系作为系统构成属性，允许将世界划分为一个系统和一个休息区。将系统组合基于可计算函数的概念及其组合行为的明显想法导致通过组合简单和递归系统形成超级系统。但是这种方法不能充分考虑以有状态和非确定性方式与许多其他系统交互的系统，这就是我引入交互和合作概念的原因。为了令人满意地描述交互系统，需要在它们与所有其他系统的关系的表示和系统内发生的事情之间取得平衡。因此，我介绍了外部交互和内部协调的互补描述，两者都基于角色概念，即系统在其交互上的投影。除了组合、合作和协调之间有趣的区别之外，所提出的方法也非常适合其他相当知名的概念。首先是组件和接口的概念。组件成为具有明确定义的组合行为的系统，因为接口概念同时捕获了系统在其交互中的转换行为和组合行为。另一个紧密相关的概念是决策和博弈。我将决策的概念作为额外的内部输入字母表引入，以确定非确定性交互，从而虚构假设系统功能，而我们实际上并不具备这样做的知识。因此，协议和游戏之间的密切关系变得显而易见。