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<Paper uid="C94-2141">
  <Title>COMPUTING FIRST AND FOLLOW FUNCTIONS FOR, FEA'rURE-THEoRE'rR? GRAMMARS</Title>
  <Section position="2" start_page="0" end_page="875" type="intro">
    <SectionTitle>
1 INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> The, need for (;flicien(; parsing is a (:onsta,n(; one in Natural Langmtge, Pro('cssing. With the advo, n|; ()f fea(;ur(&gt;l;he, ore(;i(: gratmn;ti's, In;my of (;he optimization te(:hniqu(',s that w(;re a, pi)li(:abh; to Context Free (CI&amp;quot;) grammnrs have r(;(tuircd mo(titi(:ation. For insl;an(:(~, ~ mlml)(~r of algorithms used (;o ex(;ra,(:L p;~rsing l;a~bl(~,q fl'om CF grammars have involved (list:at(ling inform~t(;ion which ol;h(',rwisc, would have constrain('d tim parsing pro('ess, (Brisco(; and Carroll, 19!)3). This t)ap(',r des(:rib(~s an extension to an algorithm that ()pe, r~L(;('~s over CF gramnmr to make, it at)pli(:M)h; to f(',atur(',-th(;oretic ()lieS. One advantage of th('~ (;x(;en(h~d Mgorithm is (;haPS it, i)r(;serves ~ts much of l;hc infOrlnalAon in (;h(! graininar as I)ossibh;.</Paragraph>
    <Paragraph position="1"> \[n order to make more t,,\[\[icient parsers, it; is SOln(;gimt',s necessary (;o pr(;process ((:Olnl)ih;) a gra, illlBa,r 1;o ext;ra,c(; \]'rom it; (;o\[)-down inforlrm~ion (;o guide (;h(; s(;mr:h during analysi.q. Tim \[irs(; sl;(;p in I;ho, prel)ro(:essing stage of several (;omi/ilal;ion algorithms requires (;h(; sohltion of (;wo \['un(',tions normally (:al\]e(l FII{,ST and F()\]AA)W. Intui(;iv(~ly, lrIILS'T(X) gives us (;h(; (;(',rmina, l symbols (;ha(; may app(;nr in hfil,ial posi(;iou in substrings de, riv(;(I froiD, c;L|;(~gory X. FOLLOW(X) gives us (;Ira (;c'rminals whi(:h may imm(;dia,t(;ly follow a su|)string o1' (:~(;e, gory X. For (,~xami)lc , in l;h(; gra,mmar S &gt; NI' VP; NP - &gt; (lel; II(tltlI; VP --} vtra NP,</Paragraph>
    <Paragraph position="3"> marks trod of input,) Th(;so, (;wo runc(;bmLs a,t:(~ hnpc, rtan|; in a \]a, rgo, l'il, II~( ~. ()f algorithms used for constructing el'licit;n(; l)arsexs. For ex;mq)le th(; l,I{-tmrse, r const, rll(stion algorithm given in (Aho c't al., 1986):232 uses FIRST to ('omt)ute item do-SllI'( ~, va, hles. AIm(;h(~r examph; is (;h{'~ t:ompu(;ation of the /* rela, tion whit:h is used in tim c(mstru('(;ion of go, nt;ralize,(1 left-(:orn(~r parsers, (N(;dcrhof, \] !)9:}); (;his relation is etl'ct:tivcly ~m ex(;ensi(m of t;h(; funt:(;ion FIRST.</Paragraph>
  </Section>
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