Non-surjectivity Our encoding, as defined formally in Section 2.1, is injective but not surjective, i.e., not every sequence of |w| − 1 labels of the form (n i , c i ) corresponds to a tree in T |w| .
there are two situations where a label sequence formally has no tree, and thus Φ −1 |w| is not formally defined and we have to use extra heuristics or processing to define it: • Sequences with conflicting nonterminals.