Zero-error capacity plays an important role in a whole range of operational tasks, in addition to the fact that it is necessary for practical applications. Due to the importance of zero-error capacity, it is necessary to investigate its algorithmic computability, as there has been no known closed formula for the zero-error capacity until now. We show that the zero-error capacity of noisy channels is not Banach-Mazur computable and therefore not Borel-Turing computable. We also investigate the relationship between the zero-error capacity of discrete memoryless channels, the Shannon capacity of graphs, and Ahlswede's characterization of the zero-error-capacity of noisy channels with respect to the maximum error capacity of 0-1-arbitrarily varying channels. We will show that important questions regarding semi-decidability are equivalent for all three capacities. So far, the Borel-Turing computability of the Shannon capacity of graphs is completely open. This is why the coupling with semi-decidability is interesting.

翻译：除了实际应用所必需的零危险能力之外,零危险能力在一系列行动任务中起着重要作用。由于零危险能力的重要性,有必要调查其算法的可计算性,因为迄今为止还没有已知的零危险能力封闭公式。我们表明,噪音频道的零危险能力不是Banach-Mazur的可计算能力,因此不是Borel-Turing的可计算能力。我们还调查了离散的无记忆频道的零危险能力、图文的香农能力以及Ahlswede关于零-eror-Captain的噪音频道特征与0-1任意性不同频道的最大误差能力之间的关系。我们将表明,关于半衰度的重要问题与所有三种能力是相等的。因此,香农能力的可计算能力波雷尔-图灵的可计算性是完全开放的。这就是为什么半衰变的合并是令人感兴趣的。