Abstract
We show that an epsilon-free, chain-free synchronous context-free grammar (SCFG) can be converted into a weakly equivalent synchronous tree-adjoining grammar (STAG) which is prefix lexicalized. This transformation at most doubles the grammar’s rank and cubes its size, but we show that in practice the size increase is only quadratic. Our results extend Greibach normal form from CFGs to SCFGs and prove new formal properties about SCFG, a formalism with many applications in natural language processing.
Highlights
Greibach normal form (GNF; Greibach, 1965) is an important construction in formal language theory which allows every context-free grammar (CFG) to be rewritten so that the first character of each rule is a terminal symbol
The remainder of this paper focuses on chain-free grammars, like (7), which cannot be converted to PL-synchronous context-free grammar (SCFG) despite containing no such cycles
We have demonstrated a method for prefix lexicalizing an SCFG by converting it to an equivalent synchronous tree-adjoining grammar (STAG)
Summary
Greibach normal form (GNF; Greibach, 1965) is an important construction in formal language theory which allows every context-free grammar (CFG) to be rewritten so that the first character of each rule is a terminal symbol. Using a prefix lexicalized grammar ensures that target sentences can be generated from left to right, which allows the use of beam search to constrain their decoder’s search space as it performs a left-to-right traversal of translation hypotheses To achieve these results, new grammars had to be heuristically constrained to include only prefix lexicalized productions, as there is at present no way to automatically convert an existing SCFG to a prefix lexicalized form. This work investigates the formal properties of prefix lexicalized synchronous grammars as employed by Watanabe et al (2006) and Siahbani et al (2013), which have received little theoretical attention compared to non-synchronous prefix lexicalized grammars. We conclude that SCFG does not have a prefix lexicalized normal form like GNF, our conversion to prefix lexicalized STAG offers a practical alternative
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