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<?xml version="1.0" standalone="yes"?> <Paper uid="C96-2123"> <Title>On the Structural Complexity of Natural Language Sentences</Title> <Section position="3" start_page="729" end_page="729" type="metho"> <SectionTitle> 2 Structural Complexity </SectionTitle> <Paragraph position="0"> The definition of structural complexity presumes the notion of dependency relationships between words in a sentence. In dependency grammars (Hudson, 1984; Mel'Suk, 1987), a dependency relationship is a primitive relationship between two words, called the head and the modifier. In constituency grammars that contain the X-bar theory as a component, dependency relationships between words are implicitly specified in X-bar structures. The modifiers of a word w are the head words of the specifier, complements, and adjuncts of w. For example, Figure 1 is the X-bar structure of (2). The word &quot;will&quot; has two modifiers: the head word ()fits NP specifier (&quot;Kinf') and the head word of its VP complement (&quot;bring&quot;). The dependency relationships in tim X-bar structure in l!'igure 1 are shown in Figure 2. Each directed link in Fignre 2 represents a dependency relationship with the direction going from the head to the modifier.</Paragraph> <Paragraph position="1"> In order to recognize the structure of a sentence, a parser must establish the dependency links between the words in the sentence. Structural complexity measures how easy or di\[\[icnlt it is to establish these dependency links. The definition of structural complexity is based on the assumption that the shorter dependency links are easier to es-tablish than longer ones, where the length of a dependency link is one plns the nmnber of words between the head and the moditier. I:or e.xample, the lengths of tile links in Figure 2 are shown by the numbers attached to the dependency links.</Paragraph> <Paragraph position="2"> Definition 2.1 (Struetural Complexity) The slructural complexity of a dependency struclure is the total length of the dependency links in the structure.</Paragraph> <Paragraph position="3"> For example the structural complexity of the dependency structure in Figure 2 is 11.</Paragraph> <Paragraph position="4"> \[n the next three sections, we will show that the definition of structural comph'.xity does i,deed retlect the difficulty in processing a sentence. We will present examples in which sentences with lower structural complexities are easier to process than similar sentences with higher structural comph;xities. null</Paragraph> </Section> <Section position="4" start_page="729" end_page="731" type="metho"> <SectionTitle> 3 Center embedding </SectionTitle> <Paragraph position="0"> The difficulty in processing center embedding senten('es: such as (13), hgs been explained by its requirement on the size of tile stack in a parsb, r.</Paragraph> <Paragraph position="1"> This explanation presumes that the human parser uses a push-down stack to store the partially built constituents. 'l'he notion of structural complexity provides an explanation of the difficulty of processing center embedding that makes much weaker commitment to the parsing model. Figure 3 shows the lengths of the dependency links in a center-embedding sentence (la) and a noncenter-embedding sentence (lb) with similar semantics. The structural complexity of the center-embedding sentence is 30, which is much higher than the structurM complexity (=112) of the noncenter-embedding sentence.</Paragraph> <Paragraph position="2"> The presumption that human sentence processor uses a push-down sl;ack is challenged by the contrast between cross-serial dependencies in Dutch (e.g., Figure 4a) and center-embedding sentences in German (e.g., Figm:e 4b.) Since the cross serial dependencies are much more ditficnlt to handle with push-down stacks</Paragraph> <Paragraph position="4"> The cat that the dog that the man bought chased died The man bought the dog that chased the cat that died The man have Hans the horses teach feed a. 1)utch: cross serial dependency, shuctuml complexity= 13 Die Maenner haben Hans die Pferde fuettern gelehrt The men have Hans the horses feed teach b. Gennan: center embedding, structural complcxily=14 The men taught Hans to feed the horses c. English: right branching, slmclural complexity=9 I&quot;igure 4: cross s(;ri31 dependency vs. ceni.er (3) a..Ioc sent \]12(; Izook he found in I)a.ris /o his pal b. Joe sent :o his pal I, he book lie found in I)3ris F, xtral)oS(~.d relative (4) a. A m3n I;h31; no one knew slood 'up h. A nr, m slood &quot;up tihal\] I10 Olle klleW I~P-(,,xtral)osition (5) a. I Feaid a. dcscril)tion of llockncy's lal,csi, l>ic(.ur(~ !lcslcrday b. 1 read a descril)t,ion ycslerday of IIo(k I(y s hi test F, icl,ure lgxl;ra('l;ion from AP (6) a.. \[low cerl,ain that the, Me~s will wi, arc</Paragraph> <Paragraph position="6"> h. I Iow certa iu a'rc '!lO~t tlmt the Mets will wi.? Me('hanislll for constraining exliraposiiiiOll iS Ill'gently ,ee(h'xl i, both parsing 3nd g~encr3l.ioll. '1'0 et),lm(l(ling ........... vs. right.-i~ra.nchillg \[ihc I)CStl of the ;ulthor's I~nowhe(lge, noue of (.Ira than nested dependeucies, the hypothesis th3t hum3n parsex uses a, push-down sta,'k would predict th3t the I)utch sentences sttch as Figure 43 shotlld be much lilt)re ditli(:ult (IC) underst3nd than the correslmnding (.lerllt3II setlLeil('es with IleSl;ec\[ (lepende~ncies (Figure 4b). Itowever, da.ta from psycho-linguistic experinlenl;s suggest (;h3t the, y a,re in fact slightly easier to proce.ss than the corresponding (;erm3n senl;ent-cs with nested de, pendencics (B3ch et 31., 1986). This obserw~,tion can be 3('counted \[or l)y structur31 complexity, since the sl;ru('tur31 comt)lcxity of the I)ut,ch sentence (Figure 4&) is 13, which is slightly lower tha,n Lhc structur31 complexity (=14) of the correspollding (~ernl3II senl.(:tlce I:'igurc 411. It was 31so el)served in (Bach et el., 1!)86) that &quot;For someone with (weu 3 limited competence in English 3nd either of the other langu3ges, the p3tterns in l)utch and Germ3n seem to be more difficult to process 3nd pro-I)road coverage parse.rs or ~ener3l,ors h3\[IdIes ex-</Paragraph> <Paragraph position="8"> ('OF this iS that exlii'a,i)osil;iOllS 3Ill)ear tO be dependent upon ccrt3in ast)ects of (:ontcxts thi{t 3re not cN)l;ured by usual synt~wtic fe3t;ures. For examt>le, compare the following 1)3Jr of sentences (7) a, I (,alked wi(;h a, m3n yesh:rda,!l with a must3che b.*l l,alked with a, ma, n one year and fo'~ur 'monihs ago wiiJi a tnjhsbw.hq The syuta, ctic struct,,,'es of (7a)3,,,I (7B)are th,, s3me, which is shown in I:igure 5, except Iiha,\[i t)he 3dwa:bial phrase Advl ) is &quot;yesterday&quot; in (7a) a, ml &quot;one year a,.d four months 3go&quot; in (71)). Although the two adw;rt)i31 phra,ses m'c two different stri.gs, ILihey a, re identical in their syntactic (~/.lltll'{~s I Yet., extr31)osition is good in (73) but b3d in (7b).</Paragraph> <Paragraph position="9"> We propose~ th3t the lmrposc of extr31)osition is to m3ke 3 sentence easier to mlderst3nd. There|'ore, ext, r3posil&m is only allowed when the structural comph~xity of l;he S(Hll;ellCe is reduced 3s a restill;. Note 1,}131, reduction of structuraJ c()mtJexity is not l, he only const, r3int on cxtr3position. '\['here are also syntactic constrains such as Right Roof Condition (Ross, 1967) or Complement Principle (Rochemont and Culicover, 1990).</Paragraph> <Paragraph position="10"> When a phrase is extraposed, the set of dependency relationships remains the same. However, the lengths of some of the dependency links will change. The structural complexity of the sentence may change as a result. Figure 6 illustrates how extrapositions atlhct the lengths of dependency links is, (3), (4), (5), and (6). Only the dependency links whose lengths are changed are shown there. In all cases, structural complexity is reduced by the extraposition.</Paragraph> <Paragraph position="11"> Consider the difference between (7a) and (7b).</Paragraph> <Paragraph position="12"> In (7a), the extraposition of \[pp with a mustache\] increases the length of the dependency link between &quot;man&quot; and &quot;with&quot; by 1, but reduces the length of the dependency between &quot;talked&quot; and &quot;yesterday&quot; by 3. Therefore, the structural complexity is reduced by 2 as a result of the extraposit,on. In contrast, in (Tb), the extraposition of \[pp with a mustache\] increases tile length of the dependency link between &quot;man&quot; and &quot;with&quot; by 6 and reduces the length of the dependency link between &quot;talk&quot; and &quot;ago&quot; by 3. Thus the structural complexity is increased when \[Pe with a mustache\] is extraposed.</Paragraph> <Paragraph position="13"> The hypothesis that extraposition must reduce the structural complexity also explains why in heavy-NP shift, the extraposed NP must be heavy, i.e., consisting of many words. When the complement Nil ) of a verb is 'shifted' to the right across an adjunct modifier of the verb, the length of the dependency link from the verb to tile head of the NP is increased by length the adjunct modifier. On the other hand, the length of the dependency link fi'om the verb to the adjunct modifier is reduced by the length of the NP. Theretbre, the structural complexity of the sentence can only be reduced as a result of the extraposition when the NP is longer than the adjunct modifier, Joe sent the book he found in Paris to his pal Joe sent to his pal the book he found in Paris</Paragraph> </Section> <Section position="5" start_page="731" end_page="732" type="metho"> <SectionTitle> 5 Linear Precedence </SectionTitle> <Paragraph position="0"> In most languages, the NP modifiers of a word tend to be <;loser to the word than it, s PP rood,tiers, which, in turn, tend to be closer to the word than its CP (clansal) modifiers. In GPSG (Gazdar et al., 1985), these lineal: order constraints are stated explicitly as the linear precedence rules. In this section, we show thai; the linear precedence rules in GPSG can be derived fl'om the assumption that the linear order among different types of modifying phrases, such as NP, PP, and CP, should minimize the structural complexity so that the sentence is as easy to process as possible.</Paragraph> <Paragraph position="1"> Suppose a word w has n modifiers XP:I, XP~, ..., XP, ; the number of words in XPi is li; mM the head word of XPi is wi, which is the pi'th word in XPi. Without loss of generality, let us assume that w precedes its modifiers. \[f the order of the modifiers is XP1, XPu, ..., XP,;, then the length of the dependency link between w and the head of XPi is (Pi + 2j-:tl lj) and the total length of dependency links within tile maximal projection of w is: -,~ \-,i- t lj \] )~,~i=l (Pi -1- L,j=I / =: (. :-l)lt + (,,.- U)l + ...+l .... , + Among all \])ert\]lltt;al;iofls Of XP I , Nit2, ..., Xl;' .... t;hc al>ove sum is tit<'+ minitnal when 11 <_ 12 <_ ... < In. In ol, her words, the total h',ngt;h of dCl)cnden<:y links is minilnal when tit<'+ modifiers with I'ewer words are <:loser to the h(;ad. (Icnerally spealdng, PPs contain more wor<ls than NPs and Cl)s con: rain more words than l.)Ps. Therefor('., Nt ) modi\[iers shouhl b<; closer 1,o t, he \]mad word t, han 1)1 > moditiers and t)l ) modifiers shoul<l be closer Lo t;h(&quot; head word t.han CI ) mo(li\[i(ws if l;hc sl;ru<:l, ural comph'.xity of tim ma.xinml pl:ojec@tu of the. \]mad word w is to be minimized.</Paragraph> </Section> class="xml-element"></Paper>