Fig. 1.

A simple PKN, the corresponding expanded hypergraph and a number of possible solutions for the obtained subgraph are shown to illustrate the association of the used weights (w) with each hyperedge. There are four options in this example: if w₁ is equal to one, ${\overline{x}}_1$ activates y. If w₂ is equal to one, ${\overline{x}}_2$ activates y. If both w₁ and w₂ are equal to one, y can be activated by ${\overline{x}}_1$ or ${\overline{x}}_2$. If w₃ is equal to one and both w₁ and w₂ are zero, ${\overline{x}}_1$ and ${\overline{x}}_2$ are required to activate y. OR gates are implicitly represented as simple edges