<?xml version="1.0" standalone="yes"?>
<Paper uid="C94-1076">
  <Title>Minimal Change and Bounded Incremental Parsing Mats Wirdn</Title>
  <Section position="7" start_page="465" end_page="466" type="concl">
    <SectionTitle>
6 Conclusions
</SectionTitle>
    <Paragraph position="0"> The boundedness criterion used here provides a guarantee that tile next update state is never more than an amount of computation away from the current state that is limited by the size of the change. This criterion is very strong. It can be thought of as constituting one ldegThls assmnption is considered too strong in reason maintenance, where, in the worst case, all formulas can be directly connected (see Goodwln \[4, page 110 f.\]). However, it seems approprlate here, since nmler a context-free grammar of the kind 'ased here only predicted edges may have mu|tlple sources. Moreover, the number of these sources is limited because of the llnearlty of the problem instance (the text).</Paragraph>
    <Paragraph position="1"> ll Since we take addition and removal of edges to be the pl'imary tasks of incremental update, we disregard the chart-preparation step. Although a more thorough analysis might take this step into &amp;ccotlnt both in the definition of g and in the complexity analysis, we do not believe that anything fundamental would be altered by this.</Paragraph>
    <Paragraph position="2">  extreme point of a continuum of ways in which to measure tile complexity of incremental algorithms. At. the other extreme, we have the option of using 11&amp;quot;1 + I,~&amp;quot;1, the cost of discarding the ohl solution and invoking a hatch-mode algorithm on the moditied problem instance. This measure might be used for showing that an algorithm with poor worst&lt;ase incremental behaviour is still practical: Poor incremental behaviour means that the algorithm does not respond quickly to (some) small changes, tlowever, it may still perform better than discarding the old solution and invoking a hatch-mode algorithm. In other words, even if the algorithm is unbounded in ~, it may have a lower time bound in IP'\[ + 1,9'1 than the batch-mode algorithm, q'he unbonn(led algorithm described ilk section 4 is an example of this: it is clearly more ellicient than the batch-mode algorithm for the lmrpose of incremental update.</Paragraph>
    <Paragraph position="3"> Several interesting topics for further research present themselves: One is to generalize the notions of minimal change and hounded incrementality to other processing frameworks that make use of a table or a chart, for example, pseudo-parallel LR. parsing (Tomita \[13\]) or taMlar generation (Neumann \[8\]). Another interesting topic is to translate the slmre notions to a unification-based grammar formalism. Defining minimal change then requires a definition of the dill'erence between two feature structures. An immediate observation is that this is itself hardly a feature structure, but rather the set of (suh)structnres that are not present in both feature structures (in analogy with our delinition of the difference between two charts).</Paragraph>
  </Section>
class="xml-element"></Paper>