Fig. 2

Both arc insertions and deletions into a BMG \((\vec {G}=(V,E),\sigma )\) can introduce inconsistencies into the set of informative triples. Top row: Leaf-colored tree \((T,\sigma )\) explaining the BMG \((\vec {G},\sigma )\). Its set of informative triples is \({\mathcal {R}}(\vec {G},\sigma )=\{ab_1|b_2,\, ab_1|b_3,\, c_1b_2|b_1,\, c_1b_3|b_1,\, c_2b_2|b_1,\, c_2b_3|b_1\}\) giving the Aho graph \(H=[{\mathcal {R}}(\vec {G},\sigma ), V]\). Bottom left: Insertion of the arc \((a, b_2)\) creates a new informative triple \(ab_2|b_3\) (\(ab_1|b_2\) gets lost) resulting in a connected Aho graph \(H'\). Bottom right: Deletion of the arc \((a, c_1)\) creates a new triple \(ac_2|c_1\) resulting in a connected Aho graph \(H''\)