高维自动机的同伦双相似性
Homotopy Bisimilarity for Higher-Dimensional Automata
摘要：
我们引入了一类新的高维自动机，其中的态射是功能同伦模拟，即功能模拟独立事件的并发性。为此，我们将高维自动机展开为高维树。利用开映射的概念，我们定义同伦双相似。我们表明，同伦双相似性是相当于一个简单的推广标准的双相似性更高的维度，它是细比分裂双相似性和不可比拟的历史保存双相似性。
英文摘要：
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is equivalent to a straight-forward generalization of standard bisimilarity to higher dimensions, and that it is finer than split bisimilarity and incomparable with history-preserving bisimilarity.
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