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<Paper uid="P91-1015">
  <Title>Head Corner Parsing for Discontinuous Constituency</Title>
  <Section position="5" start_page="119" end_page="119" type="concl">
    <SectionTitle>
4 Discussion and Extensions
</SectionTitle>
    <Paragraph position="0"> Sound and Complete. The algorithm as it is defined is sound (assuming the Prolog interpreter is sound), and complete in the usual Prolog sense.</Paragraph>
    <Paragraph position="1"> Clearly the parser may enter an infinite loop (in case non branching rules are defined that may feed themselves or in case a grammar makes a heavy use of empty categories). However, in case the parser does terminate one can be sure that it has found all solutions. Furthermore the parser is minimal in the sense that it will return one solution for each possible derivation (of course if several derivations yield identical results the parser will return this result as often as there are derivations for it).</Paragraph>
    <Paragraph position="2"> Efficiency. The parser turns out to be quite efficient in practice. There is one parameter that influences efficiency quite dramatically. If the notion 'syntactic head' implies that much syntactic information is shared between the head of a phrase and its mother, then the prediction step in the algorithm will be much better at 'predicting' the head of the phrase. If on the other hand the notion 'head' does not imply such feature percolations, then the parser must predict the head randomly from the input string as no top-down information is available.</Paragraph>
    <Paragraph position="3"> Improvements. The efficiency of the parser can be improved by common Prolog and parsing techniques. Firstly, it is possible to compile the grammar rules, lexical entries and parser a bit further by (un)folding (eg. the string predicate can be applied to each lexical entry in a compilation stage). Secondly it is possible to integrate well-formed and non-well-formed subgoal tables in the parser, following the technique described by Matsumoto et al. (1983). The usefulness of this technique strongly depends on the actual grammars that are being used. Finally, the current indexing of lexical entries is very bad indeed and can easily be improved drastically.</Paragraph>
    <Paragraph position="4"> In some grammars the string operations that are defined are not only monotonic with respect to the words they dominate, but also with respect to the order constraints that are defined between these words ('order-monotonic'). For example in Reape's sequence union operation the linear precedence constraints that are defined between elements of a daughter are by definition part of the linear precedence constraints of the mother.</Paragraph>
    <Paragraph position="5"> Note though that the analysis of verb second in the foregoing section uses a string operation that does not satisfy this restriction. For grammars that do satisfy this restriction it is possible to extend the top-down prediction possibilities by the incorporation of an extra clause in the 'connect' predicate which will check that the phrase that has been analysed up to that point can become a substring of the top string.</Paragraph>
  </Section>
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