The Artificial Hormone System (AHS) is a self-organizing middleware to allocate tasks in a distributed system. We extended it by so-called negator hormones to enable conditional task structures. However, this extension increases the computational complexity of seemingly simple decision problems in the system: In [1] and [2], we defined the problems Negator-Path and Negator-Sat and proved their NP-completeness. In this supplementary report to these papers, we show examples of Negator-Path and Negator-Sat, introduce the novel problem Negator-Stability and explain why all of these problems involving negators are hard to solve algorithmically.

中文翻译：

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人工激素系统中涉及否定关系问题的难度

人工激素系统 (AHS) 是一种自组织中间件，用于在分布式系统中分配任务。我们通过所谓的负性激素对其进行了扩展，以实现有条件的任务结构。然而，这种扩展增加了系统中看似简单的决策问题的计算复杂度：在 [1] 和 [2] 中，我们定义了问题 Negator-Path 和 Negator-Sat 并证明了它们的 NP 完备性。在这些论文的补充报告中，我们展示了 Negator-Path 和 Negator-Sat 的示例，介绍了新问题 Negator-Stability 并解释了为什么所有这些涉及否定的问题都难以通过算法解决。