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<Paper uid="P96-1016">
  <Title>Synchronous Models of Language</Title>
  <Section position="2" start_page="0" end_page="116" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Much of theoretical linguistics can be formulated in a very natural manner as stating correspondences (translations) between layers of representation; for example, related interface layers LF and PF in GB and Minimalism (Chomsky, 1993), semantic and syntactic information in HPSG (Pollard and Sag, 1994), or the different structures such as c-structure and f-structure in LFG (Bresnan and Kaplan, 1982).</Paragraph>
    <Paragraph position="1"> Similarly, many problems in natural language processing, in particular parsing and generation, can be expressed as transductions, which are calculations of such correspondences. There is therefore a great need for formal models of corresponding levels of representation, and for corresponding algorithms for transduction.</Paragraph>
    <Paragraph position="2"> Several different transduction systems have been used in the past by the computational and theoretical linguistics communities. These systems have been borrowed from translation theory, a subfield of formal language theory, or have been originally (and sometimes redundantly) developed. Finite state transducers (for an overview, see, e.g., (Aho and Ullman, 1972)) provide translations between regular languages. These devices have been popular in computational morphology and computational phonology since the early eighties (Koskenniemi, 1983; Kaplan and Kay, 1994), and more recently in parsing as well (see, e.g., (Gross, 1989; Pereira, 1991; Roche, 1993)). Pushdown transducers and syntax directed translation schemata (SDTS) (Aho and Ullman, 1969) translate between context-free languages and are therefore more powerful than finite state transducers. Pushdown transducers are a standard model for parsing, and have also been used (usually implicitly) in speech understanding.</Paragraph>
    <Paragraph position="3"> Recently, variants of SDTS have been proposed as models for simultaneously bracketing parallel corpora (Wu, 1995). Synchronization of tree adjoining grammars (TAGs) (Shieber and Schabes, 1990; Shieber, 1994) are even more powerful than the previous formalisms, and have been applied in machine translation (Abeill6, Schabes, and Joshi, 1990; Egedi and Palmer, 1994; Harbusch and Poller, 1994; Prigent, 1994), natural language generation (Shieber and Schabes, 1991), and theoretical syntax (Abeilld, 1994). The common underlying idea in all of these formalisms is to combine two generative devices through a pairing of their productions (or, in the case of the corresponding automata, of their transitions) in such a way that right-hand side nonterminal symbols in the paired productions are linked. The processes of derivation proceed synchronously in the two devices by applying the paired grammar rules only to linked nonterminals introduced previously in the derivation. The fact that the above systems all reflect the same translation technique has not always been recognized in the computational linguistics literature. Following (Shieber and Schabes, 1990) we will refer to the general approach as synchronous rewriting. While synchronous systems are becoming more and more popular, surprisingly little is known about the formal characteristics of these systems (with the exception of the finite-state devices). null In this paper, we argue that existing synchronous systems cannot handle, in a computationally attrac- null tive way, a standard problem in syntax/semantics translation, namely quantifier scoping. We propose a new system that provides a synchronization between two unordered vector grammars with dominance links (UVG-DL) (Rainbow, 1994). The type of synchronization is closely based on a previously proposed model, which we will call &amp;quot;local&amp;quot; synchronization. We argue that this synchronous system can deal with quantifier scoping in the desired way. The proposed system has the weak language preservation property, that is, the defined synchronization mechanism does not alter the weak generative capacity of the formalism being synchronized. Furthermore, the tree-to-forest translation problem for our system can be solved in polynomial time; that is, given a derivation tree obtained according to one of the synchronized grammars, we can construct the forest of all the translated derivation trees in the other grammar, using a polynomial amount of time.</Paragraph>
    <Paragraph position="4"> The structure of this paper is as follows. In Section 2, we introduce quantifier raising and review two types of synchronization and mention some new formal results. We introduce our new synchronous system in Section 3, and present our formal results and outline the proof techniques in Section 4.</Paragraph>
  </Section>
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