<?xml version="1.0" standalone="yes"?>
<Paper uid="P96-1021">
  <Title>A Polynomial-Time Algorithm for Statistical Machine Translation</Title>
  <Section position="4" start_page="152" end_page="153" type="intro">
    <SectionTitle>
2 ITG and BTG Overview
</SectionTitle>
    <Paragraph position="0"> The new translation model is based on the recently introduced bilingual language modeling approach.</Paragraph>
    <Paragraph position="1"> Specifically, the model employs a bracketing transduction grammar or BTG (Wu, 1995a), which is a special case of inversion transduction grammars or ITGs (Wu, 1995c; Wu, 1995c; Wu, 1995b; Wu, 1995d). These formalisms were originally developed for the purpose of parallel corpus annotation, with applications for bracketing, alignment, and segmentation. This paper finds they are also useful for the translation system itself. In this section we summarize the main properties of BTGs and ITGs.</Paragraph>
    <Paragraph position="2"> An ITG consists of context-free productions where terminal symbols come in couples, for example x/y, where z is a Chinese word and y is an English translation of x. 2 Any parse tree thus generates two strings, one on the Chinese stream and one on the English stream. Thus, the tree: (1) \[~/I liST/took \[--/a $:/e ~t/book\]Np \]vP \[,,~/for ~/you\]pp \]vP Is produces, for example, the mutual translations: (2) a. \[~ \[\[ST \[--*~\]NP \]vP \[~\]PP \]vP Is \[W6 \[\[nA le \[yi b~n shfi\]Np \]vp \[g@i ni\]pp \]vP \]s b. \[I \[\[took \[a book\]Np \]vP \[for you\]pp \]vP Is An additional mechanism accommodates a conservative degree of word-order variation between the two languages. With each production of the grammar is associated either a straight orientation or an inverted orientation, respectively denoted as follows:</Paragraph>
    <Paragraph position="4"> In the case of a production with straight orientation, the right-hand-side symbols are visited left-to-right for both the Chinese and English streams.</Paragraph>
    <Paragraph position="5"> But for a production with inverted orientation, the 2Readers of the papers cited above should note that we have switched the roles of English and Chinese here, which helps simplify the presentation of the new translation algorithm.</Paragraph>
    <Paragraph position="6">  sentences of length f, with and without the BTG restriction.</Paragraph>
    <Paragraph position="7"> right-hand-side symbols are visited left-to-right for Chinese and right-to-left for English. Thus, the tree:  (3) \[~/I (\[,.~/for ~/you\]pp \[$~'/took \[--/a ak/e ~idt/book\]Np \]vp )vP \]s produces translations with different word order: (4) a. \[~J~ \[\[,,~*l~\]pp \[~Y \[--2\[~-~\]Np \]VP \]VP \]S b. \[I \[\[took \[a book\]Np \]vP \[for you\]pp \]vP \]s  In the special case of BTGs which are employed in the model presented below, there is only one undifferentiated nonterminal category (aside from the start symbol). Designating this category A, this means all non-lexical productions are of one of these two forms: A ---+ \[AA...A\] A ---+ (AA...A} The degree of word-order flexibility is the critical point. BTGs make a favorable trade-off between efficiency and expressiveness: constraints are strong enough to allow algorithms to operate efficiently, but without so much loss of expressiveness as to hinder useful translation. We summarize here; details are given elsewhere (Wu, 1995b).</Paragraph>
    <Paragraph position="8"> With regard to efficiency, Figure 2 demonstrates the kind of reduction that BTGs obtain in the space of possible alignments. The number of possible alignments, compared against the unrestricted case where any English word may align to any Chinese position, drops off dramatically for strings longer than four words. (This table makes the simplification of counting only 1-1 matchings and is merely representative.) With regard to expressiveness, we believe that almost all variation in the order of arguments in a syntactic frame can be accommodated, a Syntactic frames generally contain four or fewer subconstituents. Figure 2 shows that for the case of four subconstituents, BTGs permit 22 out of the 24 possible alignments. The only prohibited arrangements are &amp;quot;inside-out&amp;quot; transformations (Wu, 1995b), which we have been unable to find any examples of in our corpus. Moreover, extremely distorted alignments can be handled by BTGs (Wu, 1995c), without resorting to the unrestricted-alignment model.</Paragraph>
    <Paragraph position="9"> The translation expressiveness of BTGs is by no means perfect. They are nonetheless proving very useful in applications and are substantially more feasible than previous models. In our previous corpus analysis applications, any expressiveness limitations were easily tolerable since degradation was graceful. In the present translation application, any expressiveness limitation simply means that certain translations are not considered.</Paragraph>
    <Paragraph position="10"> For the remainder of the paper, we take advantage of a convenient normal-form theorem (Wu, 1995a) that allows us to assume without loss of generality that the BTG only contains the binary-branching form for the non-lexicM productions. 4</Paragraph>
  </Section>
class="xml-element"></Paper>