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<Paper uid="W05-1507">
  <Title>Machine Translation as Lexicalized Parsing with Hooks</Title>
  <Section position="6" start_page="69" end_page="72" type="concl">
    <SectionTitle>
7 Conclusion
</SectionTitle>
    <Paragraph position="0"> By showing the parallels between lexicalization for language model state and lexicalization for syntactic heads, we have demonstrated more efficient algorithms for previously described models of machine translation. Decoding for Inversion Transduction Grammar with a bigram language model can be done in O(n6) time. This is the same complexity as the ITG alignment algorithm used by Wu (1997) and others, meaning complete Viterbi decoding is possible without pruning for realistic-length sentences. More generally, ITG with an m-gram language model is O(n3+3(m[?]1)), and a synchronous context-free grammar with at most R spans in the input language is O(n3(m[?]1)+(2R+1)). While this improves on previous algorithms, the degree in n is probably still too high for complete search to be practical with such models. The interaction of the hook technique with pruning is an interesting  Algorithm 1 ITGDecode(Nt) for all s, t such that 0 [?] s &lt; t [?] Nt do for all S such that s &lt; S &lt; t do a3 straight rule for all rules X - [Y Z] [?] G do for all (Y, u1, v1) possible for the span of (s, S) do a3 a hook who is on (S, t), nonterminal as Z, and outside expectation being v1 is required if not exist hooks(S, t, Z, v1) then build hooks(S, t, Z, v1) end if for all v2 possible for the hooks in (S, t, Z, v1) do a3 combining a hook and a hypothesis, using straight rule b(s, t, X, u1, v2) =  for all rules X - &lt;Y Z&gt; [?] G do for all (Z, u2, v2) possible for the span of (S, t) do a3 a hook who is on (s, S), nonterminal as Y , and outside expectation being v2 is required if not exist hooks(s, S, Y, v2) then build hooks(s, S, Y, v2) end if for all v1 possible for the hooks in (s, S, Y, v2) do a3 combining a hook and a hypothesis, using inverted rule b(s, t, X, u2, v1) =  area for future work. Building the chart items with hooks may take more time than it saves if many of the hooks are never combined with complete constituents due to aggressive pruning. However, it may be possible to look at the contents of the chart in order to build only those hooks which are likely to be useful.</Paragraph>
  </Section>
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