For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-outsubgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.

中文翻译：

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同伴和反应系统的基本运动

对于一组集合，我们将元素视为与同伴属于同一集合的元素。反应系统的整体动力学（由Ehrenfeucht和Rozenberg引入）可以用有向图表示，称为有向图，该图由一个单子图（称为0上下文图）唯一确定。我们考虑过渡图开始时的伴随类，并引入有向多重图，称为基本运动，其顶点就是此类伴随类。我们表明，从基本运动中获得的所有一次性图形都表示具有同构过渡图的反应系统的0上下文图。通过交换陪伴顶点的输出边缘，可以相互获取所有此类0背景图。