The celebrated 1999 Asynchronous Computability Theorem (ACT) of Herlihy and Shavit characterized the distributed tasks that are wait-free solvable, and thus uncovered a deep connection with algebraic topology. We present a novel interpretation of this theorem, through the notion of continuous task, defined by an input/output specification that is a continuous function. To do so, we introduce a chromatic version of a foundational result for algebraic topology: the simplicial approximation theorem. In addition to providing a different proof of the ACT, the notion of continuous task seems interesting in itself. Indeed, besides the fact that certain distributed problems are naturally specified by continuous functions, continuous tasks have an expressive power that also allows to specify the density of desired outputs for each combination of possible inputs,for example.

翻译：1999年赫利希和沙维特著名的1999年热利希和沙维特的Asyncronous Compunity Theorem(ACT)对分布式任务作了说明,这些任务是无等待可溶的,因此发现了与代数地形学的深层联系。我们通过连续任务的概念对这一理论作了新的解释,这种任务的定义是输入/产出的规格,这是一个连续的功能。为此,我们为代数表层学引入了一个基本结果的染色版:简化近似理论。除了提供不同的证据外,连续任务的概念本身也似乎很有趣。 事实上,除了某些分布式的问题自然地由连续的功能来说明外,连续的任务还具有一种清晰的表达力,能够为每一种可能的投入组合确定预期产出的密度,例如。