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<Paper uid="E06-1004">
  <Title>Computational Complexity of Statistical Machine Translation</Title>
  <Section position="8" start_page="30" end_page="31" type="concl">
    <SectionTitle>
5 Conclusions
</SectionTitle>
    <Paragraph position="0"> IBM models 3-5 are widely used in SMT. The computational tasks discussed in this work form the backbone of all SMT systems that use IBM models. We believe that our results on the computational complexity of the tasks in SMT will result in a better understanding of these tasks from a theoretical perspective. We also believe that our results may help in the design of effective heuristics  for some of these tasks. A theoretical analysis of the commonly employed heuristics will also be of interest.</Paragraph>
    <Paragraph position="1"> An open question in SMT is whether there existsclosed formexpressions (whoserepresentation is polynomial in the size of the input) for P (f|e) and the counts in the EM iterations for models 3-5 (Brown et al., 1993). For models 1-2, closed form expressions exist for P (f|e) and the counts in the EM iterations for models 3-5. Our results show that there cannot exist a closed form expression (whose representation is polynomial in the size of the input) for P (f|e) and the counts in the EM iterations for Models 3-5 unless P = NP.</Paragraph>
  </Section>
class="xml-element"></Paper>