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<Paper uid="C96-1076">
  <Title>Modularizing Contexted Constraints</Title>
  <Section position="2" start_page="0" end_page="448" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> There are two facts that conspire to make tile treatment of disjunction an important consideration when building a natural language processing (NLP) system. The first fact is that natural languages are full of ambiguities, and in a grammar many of these ambiguities are described by disjunctions. The second fact is that the introduction of disjmmtion into a grammar causes processing tilne to increase exponentially in the number of disjunets. This means that a nearly linear-time operation, such as uififieation of Imrely conjunctive feature structures, becomes an exponential-time problem as soon as disjunctions are included, t Since disjunction is unlikely to dis* This work was sponsored by Teilprojekt B4 &amp;quot;t~Y=om Constraints to Rules: Compilation of lipS(;&amp;quot; of the Sonderforsehungsbereieh 340 of the Deutsche Forsehungsgemeinschaft. I would also like to thank Dale Gerdemann and Guido Minnen for helpfltl comments on the ideas presented here. All remaining errors are of course my own.</Paragraph>
    <Paragraph position="1"> tAssuming P # NIL appear from natur~fl language gralnlnars, controlling its form (:all save exponential amounts of time. This paper introduces all etficient normal tbrm for processing dependent disjunctive constraints and an operation for compilation into this normal form. This ot)eration , modularization, can reduce exponential alnounts of redtmdant information in a grainmar and can consequently save corresponding alnounts of processing time. While this operation is general enough to be applied to a wide variety of constraint systems, it; was originally designed to optimize processing of dependent disjunctions in featm'e structure-based grammars. In particular, modular fea.tuie structures are more eflicient R)r unification than non-Inodulm' ones.</Paragraph>
    <Paragraph position="2"> Since ill many current NLP systems, a signiticant amount of tilne is spent performing unification, optimizing feature structures for unillcatioll shouhl increase the tmrtbrmance of these, syst;ems.</Paragraph>
    <Paragraph position="3"> Many algorithms for etticient mfitication of lea tare structures with dependent disjunctions have been propose.d (Maxwell and Kaplan, 1989; F, isele and DSrre, 1990; Gerdemann, 1991; StrSmbSek, 1992; Griflith, 1.996). However, all of these algorithms sutfer from a common problem: thc.ir performance is highly deternfined by their inputs.</Paragraph>
    <Paragraph position="4"> All of these algorithms will perform at their best when their dependent disjunctions interact as little as possible, but if all of the disjunctions interact, then these algorithms may perform redundant computations. The need for ef\[icient inputs has been noted in the literature 2 but there have been few attempts to automatically optilnize gr;mnnars tor disjunetiw; unification algorithms.</Paragraph>
    <Paragraph position="5"> The modularization algorithm presented in this paper takes existing dependent disjunctions and splits them into independent groups by deterlnining which disjunctions really interact. Indel}endent groups of disjunctions can be processed separat;ely during unification rathe, r than having to try every combination of one group with every combination of every other group.</Paragraph>
    <Paragraph position="6"> This pat)er is organized as follows: Section 2 gives an informal introduction to dependent dis~Cf. (Maxwell and Kaplan, \]991) fl)r instance.</Paragraph>
    <Paragraph position="7">  juncl;ions and shows how r(,ctundani; int(;raclli(lns lml,w(;en groups of (tisju:n(:l;ions (:mi bc r(;du(:ed. S(;c:i;ion 3 shows how normal disjunctions c;m t)(; r(;l)lac(;d t)y (:ont, cxtx;d constrainl:s. S(,(:tion 4 t;hcn ,&lt;d~ows how t, hcs('~ cont(;xl;(',d (',onstraints can encod(, del)(',nd(;ni, disjunctions. S(!(:l;ion 5 1)r(!s(',nts the mo(hllm'ization a,lgorii;hm for conlx~xi;ed (',on-. si;ra.ini;s. Ih)wever, e, ven though this algor{l;hm is t~ (;omt)ih&gt;t,im(', ot)(;ralJ(m , it itself has (;xt)on(nitial comt)lexity, so lilil, l(ing it IllOl(', (~tli(',i(mi; should ~Jso 1)(; a (:onc:(,rn. A i;h(~or(;m will l,hc, Ii \])(; i)r(~s(mix;d ill S('x'J;iOll (i t\]mL t)(!rllli(;s ;I, li (',xt)olt(!tll;ial t)&amp;rt; ()\[ i,tl(; nm(hllarizal;ion algo\]'il,hm I;()I)c rct)l;t(:(',(l 1 W combinatorial aam.lysis.</Paragraph>
  </Section>
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