<?xml version="1.0" standalone="yes"?>
<Paper uid="P96-1034">
  <Title>Efficient Transformation-Based Parsing</Title>
  <Section position="6" start_page="260" end_page="261" type="concl">
    <SectionTitle>
5 Discussion
</SectionTitle>
    <Paragraph position="0"> In this section we relate our work with the existing literature and further discuss our result.</Paragraph>
    <Paragraph position="1"> There are several alternative ways in which one could see transformation-based rewriting systems.</Paragraph>
    <Paragraph position="2"> TTS's are closely related to a class of graph rewr.iting systems called neighbourhood-controlled embedding graph grammars (N CE grammars; see (J anssens and Rozenberg, 1982)). In fact our definition of the relation and of the underlying \[/\] operator has been inspired by similar definitions in the NCE formalism. Apart from the restriction to tree rewriting, the main difference between NCE grammars and TTS's is that in the latter formalism the productions are totally ordered, therefore there is no recursion.</Paragraph>
    <Paragraph position="3"> Ordered trees can also be seen as ground terms. If we extend the alphabet ~ with variable symbols, we can redefine the ~ relation through variable substitution. In this way a TTS becomes a particular kind of term-rewriting system. The idea of imposing a total order on the rules of a term-rewriting system can be found in the literature, but in these cases all rules are reconsidered for application at each step in the rewriting, using their priority (see for instance the priority term-rewriting systems (Baeten, Bergstra, and Klop, 1987)). Therefore these systems allow recursion. There are cases in which a critical rule in a TTS does not give rise to order-dependency in rewriting. Methods for deciding the confluency property for a term-rewriting system with critical pairs (see (Dershowitz and Jouannaud, 1990) for definitions and an overview) can also be used to detect the above cases for TTS.</Paragraph>
    <Paragraph position="4"> As already pointed out, the translation problem investigated here is closely related with the standard tree pattern matching problem. Our automata AG (Definition 3) can be seen as an abstraction of the bottom-up tree pattern matching algorithm presented in (Hoffmann and O'Donnell, 1982). While that result uses a representation of the pattern set  (our set lhs(R)) requiring an amount of space which is exponential in the degree of the pattern trees, as an improvement, our transition function does not depend on this parameter. However, in the worst case the space requirements of both algorithm are exponential in the number of nodes in lhs(R) (see the analysis in (Hoffmann and O'Donnell, 1982)). As already discussed in Section 3, the worst case condition is hardly met in natural language applications. Polynomial space requirements can be guaranteed if one switches to top-down tree pattern matching algorithms. One such a method is reported in (Hoffmann and O'Donnell, 1982), but in this case the running-time of Algorithm 1 cannot be maintained.</Paragraph>
    <Paragraph position="5"> Faster top-down matching algorithms have been reported in (Kosaraju, 1989) and (Dubiner, Galil, and Magen, 1994), but these methods seems impractical, due to very large hidden constants.</Paragraph>
    <Paragraph position="6"> A tree-based extension of the very fast algorithm described in (Roche and Schabes, 1995) is in principle possible for transformation-based parsing, but is likely to result in huge space requirements and seems impractical. The algorithm presented here might then be a good compromise between fast parsing and reasonable space requirements.</Paragraph>
    <Paragraph position="7"> When restricted to monadic trees, our automaton Ac comes down to the finite state device used in the well-known string pattern matching algorithm of Aho and Corasick (see (Aho and Corasick, 1975)), requiring linear space only. If space requirements are of primary importance or when the rule set is very large, our method can then be considered for string-based transformation rewriting as an alternative to the already mentioned method in (Roche and Schabes, 1995), which is faster but has more onerous space requirements.</Paragraph>
  </Section>
class="xml-element"></Paper>