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<Paper uid="P03-2003">
  <Title>On the Applicability of Global Index Grammars</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The notion of Mildly context-sensitivity was introduced in (Joshi, 1985) as a possible model to express the required properties of formalisms that might describe Natural Language (NL) phenomena. It requires three properties:1 a) constant growth property (or the stronger semi- null gian Case and Chinese numbers) might be considered to be beyond certain mildly context-sensitive formalisms. TALs/LILs) is able to capture up to 4 counting dependencies (includes L4 = fanbncndnjn , 1g but not L5 = fanbncndnenjn , 1g). They were proven to have recognition algorithms with time complexity O(n6) (Satta, 1994). In general for a level-k MCSL the recognition problem is in O(n3C/2k!1) and the descriptive power regarding counting dependencies is 2k (Weir, 1988). Even the descriptive power of level-2 MCSLs (Tree Adjoining Grammars (TAGs), Linear Indexed Grammars (LIGs), Combinatory Categorial Grammars (CCGs) might be considered insufficient for some NL problems, therefore there have been many proposals3 to extend or modify them. On our view the possibility of modeling coordination phenomena is probably the most crucial in this respect.</Paragraph>
    <Paragraph position="1"> In (Casta~no, 2003) we introduced Global Index Grammars (GIGs) - and GILs the corresponding languages - as an alternative grammar formalism that has a restricted context sensitive power. We showed that GIGs have enough descriptive power to capture the three phenomena mentioned above (reduplication, multiple agreements, crossed agreements) in their generalized forms. Recognition of the language generated by a GIG is in bounded polynomial time: O(n6).</Paragraph>
    <Paragraph position="2"> We presented a Chomsky-Sch&amp;quot;utzenberger representation theorem for GILs. In (Casta~no, 2003c) we presented the equivalent automaton model: LR-2PDA and provided a characterization the3There are extensions or modifications of TAGs, CCGs, IGs, and many other proposals that would be impossible to mention here.</Paragraph>
    <Paragraph position="3"> orems of GILs in terms of the LR-2PDA and GIGs. The family of GILs is an Abstract Family of Language.</Paragraph>
    <Paragraph position="4"> The goal of this paper is to show the relevance of GIGs for NL modeling and processing. This should not be understood as claim to propose GIGs as a grammar model with &amp;quot;linguistic content&amp;quot; that competes with grammar models such as HPSG or LFG. It should be rather seen as a formal language resource which can be used to model and process NL phenomena beyond context free, or beyond the level-2 MCSLs (like those mentioned above) or to compile grammars created in other framework into GIGs. LIGs played a similar role to model the treatment of the SLASH feature in GPSGs and HPSGs, and to compile TAGs for parsing. GIGs offer additional descriptive power as compared to LIGs or TAGs regarding the canonical NL problems mentioned above, and the same computational cost in terms of asymptotic complexity. They also offer additional descriptive power in terms of the structural descriptions they can generate for the same set of string languages, being able to produce dependent paths.4 This paper is organized as follows: section 2 reviews Global Index Grammars and their properties and we give examples of its weak descriptive power. Section 3 discusses the relevance of the strong descriptive power of GIGs. We discuss the structural description for the palindrome, copy and the multiple copies languages fww+jw 2 S/g. Finally in section 4 we discuss how this descriptive power can be used to encode HPSGs schemata.</Paragraph>
  </Section>
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