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<Paper uid="C94-1065">
  <Title>LIl~(k)- I'msing of C( ut 1 A-Cont(xt,-\]~ (c Grammars :) -) 0 &amp;quot; ~ ~ ~ '~* ~ *</Title>
  <Section position="7" start_page="403" end_page="404" type="concl">
    <SectionTitle>
13 q?he Definition
</SectionTitle>
    <Paragraph position="0"> Go far, we. did not discuss the situation that there /tre distinct transitions fitting for the same state in DFA((\[).</Paragraph>
    <Paragraph position="1"> S h if t- Red u ce and Red nce- Red u(:e con flic ts are for bklde.n as they are for Cl&amp;quot;(\]s. The new conflicts result if we have to decide whether we. push &amp;~(q,,,,, fj), fj e CI&amp;quot;(P), or Shift resp. Reduce as usual. If a state q shows such a &lt;'llew&amp;quot; conflict, it contains two items of the kind \[Zi -~ 7i.Yflli\] and \[Xt ---* (tt.~fll\], ~ Q :\[', or \[XI -* (~t.\]. ~l'his is easy to deeide as far as we are wadking on future, since tile inforlllatiolI llecessal'y is store.d there, r\]'}lllSl We only \],ave a real con\[\[let if&amp;quot; i = 1 :tnd l =: 1 holds for the M)ove items.</Paragraph>
    <Paragraph position="2"> Obviolmly, this cannot })e decided determinlstically, sluce we would h:tve to know about the structure of the derivation tree not constructed so far. E.g., in the first conflict, we wouhl \]lave to s;ty whether ~&amp;quot; is ,~ son of )~ (cltoose &amp;;(q,) 5 .... 21(f,))) or whet|let e is a son of X, (choose 8c:(q,~)). It follows that( we need a modified dclinitio,I of &amp;quot;conllicts&amp;quot; compared to CI;'Cs.</Paragraph>
    <Paragraph position="3">  need a Ct)llStltllt itlllOllllt Of additional steps per eontextfi'ce step lor past and fulure. DI,'A(G) is determined only once for each G'. The VPP hohls since it holds for tlle contcxt-fi'ec algorithm and fldure additionally e.sures that tim ctmpling is correct. ~1 LR(k)- (?oupled-Context..l&amp;quot;ree (lI';tllllll~tl'S l'CSIlIl~ \[lOm the above by resolving conflicts in I)I&amp;quot;A((;) by addi.g st h)okahead set to tim items which are involved in it conflict. For this purpose, we lsse Lhe m;tpphtgs b'll~ST'~ ~tst(I l&amp;quot;OLLOWk as defined fin&amp;quot; LL(k) ~ (\]Oul)led-Context-Free Grammars in \[Pit94\]. There, these mappings are generalized such that they take the couplinl, Imtween the eOllll)otleltts of each lloiaterlllilla\] ilttoo ;I.CCOIIIS~, illSte;td o\[ working simply on C/&amp;quot;(G). Thus, we tre;tt only colnplete parentheses as ~t context-free IiotltersIlillal itlld the i'(~Slllt is much ltlo|:e ex~Lct as, e.g., ill \[SVgl)\]. This results in an adequate generalization of the LR(k)-notion for CCI&amp;quot;C.</Paragraph>
    <Paragraph position="4"> s .... w,- 12x@_, x ~~~;?v/\] Ix .... t, r&amp;quot;l. t &amp;quot; i.l ....</Paragraph>
    <Paragraph position="5"> L;- ..... l q,, - .... x.,,l \[,- ...... l \] \[.,. ,,,.,..,l\] ,I -:l .\[ '1 \[-C-:J:~Z:j IA;:Y, Sbq I~;,),(1 \[:Y=;-,,:,~:~.J Example 2 The lanyuage {a&amp;quot;b&amp;quot;c&amp;quot;d'* \] &amp;quot;n &gt; l} generalcd by the gmut.u.&amp;quot; in l'):rttmple 1 shows the .LR(O)-properly.</Paragraph>
    <Paragraph position="6"> DFA(G) is shown i. Figure 4.</Paragraph>
    <Paragraph position="7"> l~x,~,~q,h, :t 7'/,e: l.,,.,,.:., (,w$,,, lw ~ {., ~,}') .,o&amp;ni,,q cross-seri(d dcpemh'ncics c.n be .qencroled by lhe L R( l )r..,,.,.,s. ({s, (._5 x)), {,,., I,},/', s) ~ C/cro(2) ,,..,,e P :: {s-~ x,x, (x, x)-~ (.x, ,,x) lO, x, ~x)I (~, ~:)}.</Paragraph>
  </Section>
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