Each synchronous production (i.e., rule) rewrites a nonterminal into a pair of strings, γ and α, where γ (or α) contains terminal and nonterminal symbols from the source (or target) language and there is a one-toone correspondence between the nonterminal symbols on both sides.
the hierarchical model (Chiang, 2007) studied in this paper explores hierarchical structures of natural language and utilize only a unified nonterminal symbol X in the grammar, where ∼ is the one-to-one correspondence between X's in γ and α, and it can be indicated by underscripted co-indexes.