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<Paper uid="P96-1021">
  <Title>A Polynomial-Time Algorithm for Statistical Machine Translation</Title>
  <Section position="8" start_page="156" end_page="157" type="concl">
    <SectionTitle>
6 Conclusion
</SectionTitle>
    <Paragraph position="0"> We have introduced a new algorithm for the run-time optimization step in statistical machine translation systems, whose polynomial-time complexity addresses one of the primary obstacles to practicality facing statistical MT. The underlying model for the algorithm is a combination of the stochastic BTG and bigram models. The improvement in speed does not appear to impair accuracy significantly.</Paragraph>
    <Paragraph position="1"> We have implemented a version that accepts ITGs rather than BTGs, and plan to experiment with more heavily structured models. However, it is important to note that the search complexity rises exponentially rather than polynomially with the size of the grammar, just as for context-free parsing (Barton, Berwick, and Ristad, 1987). This is not relevant to the BTG-based model we have described since its grammar size is fixed; in fact the BTG's minimal grammar size has been an important advantage over more linguistically-motivated ITG-based models.</Paragraph>
    <Paragraph position="2">  We have also implemented a generalized version that accepts arbitrary grammars not restricted to normal form, with two motivations. The pragmatic benefit is that structured grammars become easier to write, and more concise. The expressiveness benefit is that a wider family of probability distributions can be written. As stated earlier, the normal form theorem guarantees that the same set of shapes will be explored by our search algorithm, regardless of whether a binary-branching BTG or an arbitrary BTG is used. But it may sometimes be useful to place probabilities on n-ary productions that vary with n in a way that cannot be expressed by composing binary productions; for example one might wish to encourage longer straight productions. The generalized version permits such strategies.</Paragraph>
    <Paragraph position="3"> Currently we are evaluating robustness extensions of the algorithm that permit words suggested by the language model to be inserted in the output sentence, which the original A* algorithms permitted.</Paragraph>
  </Section>
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