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<Paper uid="C96-1028">
  <Title>Cross-Serial Dependencies Are Not Hard to Process</Title>
  <Section position="6" start_page="160" end_page="161" type="concl">
    <SectionTitle>
4 Discussion
</SectionTitle>
    <Paragraph position="0"> Tile context; free languages have alre.ady been studied from the perspective of minimal addition to incorporate copy languages. Savitch (1989) does exactly that by prese, nting the model of con&gt; put;at|on required for the class of languages delined by augment;ing the CFLs with redut)lication: a Reduplicat;ion PDA (RPDA). An I~PDA is just a PDA which has a special type of symbol thai, can tie put onto the stack to nlake the machine treat the part of the stack above it ms if it were a queue. Essentially, t,his obtains the reversM behavior nee, ded of a st.ack to process copy languages as well as rew',rsals. Mull,|pie instances of the special sylnbol can be placed on |.he stack. Sayitch present,s a chara.ct,erization of the languages ill te, rms of stxingsets and the requisil;e compu-Lal;ional structures. The family that we characterized above in terms of graInntars arc tn'operly a sullset of the languages recognized by R.PDA, a restrk:tion of RPDA languages which Savitch (1989) terlns simple R, PDA lanqu,.qes. The model of comput~ttion here is an RPDA in which only (me spe, cial symbol is allowed on the stack at any one, time. We have not In'oven the equivalence we conje(:tllre bel, we(,'tl our Inetagranunatical method and the reduplication contex&amp;free grammars (RCFC, s) that Savi|,ch introduces as generative of simple RPDA languages. Saviteh's (1989) grammars are stated in terms of rule schemata (a tin|re set) that general,e potentially infinite sets of rewril;e rules. This is the tradeoff lletwe, en doing things metagraInmatieally and directly.</Paragraph>
    <Paragraph position="1"> Josh |and Rainbow (Josh|, 1990; Rainbow and Josh|, 1994) have also considered the perforntan('e data associated with processing crossed vs. nested dependencies and present an alternative computal, ion model, |;tie bottom-up embedded PDA (BEPDA), designed for a wit|an|; of tree-adjoining gralnmar (it uses a stack of slacks and a more complex operation for eml)tying the stack). II,ambow an(1 Josh |(1994) use the processing model to demonstrate that it can account for the dilDrence between crossed and nested dependencies in terlns of the amount of time associated objects spend in the pushdown store of the BEPDA using a mildly context free language model that captures dependencies directly, rather t;han metagrammatically. 7 r Josh |(1990) gives a similar analysis fi)r EDPAs.</Paragraph>
    <Paragraph position="2"> Essentially, their analysis (:oncludes (;tie satne: when judging string isomorphisnls, it; is easier to make the judgment of identic~flly ordered pairs than it is to reversely ordered pairs. Thus, the cross-serial dependencies needn't cost the worst ease complexity for parsing indexed or mildly ecrutext sensitive languages. Parsing ww languages requires, at worst, (;lie worst ease complexity of parsing w in whichever language class w is restricted to. Shieber (1985) pointed out without proof that (;tie nonCl,' data associated ZiMch di-Nee(; is linearly parsable; our task has been to clarify how this follows from the language (;heory.</Paragraph>
    <Section position="1" start_page="160" end_page="160" type="sub_section">
      <SectionTitle>
4.1 A Caveat
</SectionTitle>
      <Paragraph position="0"> For eilicicnt processing of ww to entail correspond~ ing eomplexity fin&amp;quot; natural lmlguages that license cross-serial dependencies hinges crucially on there being eflMently (:(mlputable hoinonmrphisms tmtween the natural language, and the string duplieati&lt;m languages. This is aIl open question, tIowever, given that empirical work that COlnpares processing of crossed atld nested dependencies alld concludes that the m'oss-serial dependencies are preferred to nested ones (Bach el; al., 1986), and giw~,n (}tit' arl{un!.ent thai, cross-serial dependencies are in theory easier to process, we feel it. teas(mable to enterta.in the asSUml)tion that somel;hing such exists. This does n(~t require us l.(~ assunlo thai; ileol)le a(:Lually use conl,exl;-fl'ee grammars and COlllp/lte holllolnort)hisills ill order 1,o itnderstand natural languages, just thai; l:he c(mlt)ul;ational model should lm at least approximat.ely as eflicient as t)eoph~,.</Paragraph>
    </Section>
    <Section position="2" start_page="160" end_page="161" type="sub_section">
      <SectionTitle>
4.2 ImI)lications
</SectionTitle>
      <Paragraph position="0"> ()tit' inetagralnmatical approach to dealing with cross serial dependencies involves the ~uSSUlnpl,ion of an operation for testing string duplication. We hinl;ed earlier that we h;el there to lm sutlicient reason to believe that copy-checldng is a basic cognitive flmction, and although we don't suppose that, people have built in production systems and processors isolnorphic to ollr chart parser aim base language, we do think that t,his copy-dmeking is invoked in the processing of crossed depe.Ildencies.</Paragraph>
      <Paragraph position="1"> Our approach to accounting for the processing complexity that the string duplication languages should take does make empMcal predictions and these can lie teste, d. For instance, if it is t;he case that such a nmchanisin exists, then patterns of string-copy disthtency should ocellr with (lifferenl.</Paragraph>
      <Paragraph position="2"> frequency in languages that lk:ense cross-serial (lependencies than in those tha, t (t(I iI.ot. A stxingcopy dislhleney is just one that involves a repeat of part of the sentence, ul, t;ered so far: 1. We went to the to lhe store to buy some Jlo'.a'.</Paragraph>
      <Paragraph position="3"> The idea ix that speakers of bmguages with ww homomorphisms have a different pattenl of invoking copy-checking than those who speak lan- null guages that do not admit cross serial dependencies. These differences should be manifest in speech corpora like those that are currently being accumulated (Anderson et al., 1992; Miller, 1995), but which n~d augmentation by a corpus derived from copy-language dialects. Verifying this would, for example, establish whether the copied strings need to be constituents, and this has a bearing on whether processing models designed for incremental interpretation (Milward, 1992) are the best descriptors of human performance.&amp;quot; We do not offer arguments that our metagrammatical approach is the best description of human processing of cross-serial dependencies, just that it is another theoretical justification for the difference in processing nested dependencies and efficient processing of crossed dependencies.</Paragraph>
    </Section>
  </Section>
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