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

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