On the Hardness of Problems Involving Negator Relationships in an Artificial Hormone System

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.