We to refer to the individual components of a path p. In addition, define S N to be the set of states in S of the form a, b (as opposed to the form c ↓ or c ↑ where c ∈ V L ).
we now define a new index set, I = V ∪ E ∪ S N ∪ P, adding variables y s for s ∈ S N , and y p for p ∈ P. If we take Y ⊂ {0, 1} |I| to be the set of valid derivations, the optimization problem is to find y * = arg max y∈Y f (y), where f (y) = θ • y, that is, we might define θ s = 0 for all s, and The y v and y e variables form a valid derivation in the original hypergraph.