Using the Index

For TFSGs, using a positional index key for each daughter presents the advantage of not needing an indexing (hash) function during parsing for the TFSs themselves (a discussion of when positional indexing is not a good solution is given in Section 7.4.2). When a rule is extended during parsing, a matching edge for each daughter is looked up in the chart. The position of the daughter $(R_i,D_j)$ acts as the index key, and matching edges are searched for only in the list indicated by the key $(R_i,D_j)$.