Abstract
More and more often, in real-word natural language processing (NLP) applications based upon grammars, these grammars are no longer written by hand, but are automatically generated. This chapter will consider one of the consequences of this state of affairs: the generated grammars may be very large. Indeed, we aim to deal with grammars that might have over a million symbol occurrences and several hundred thousands rules. Traditional parsers are not usually prepared to handle them, either because these grammars are simply too big (the parser’s internal structures blow up) or the time spent to analyze a sentence becomes prohibitive.
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- 1.
In the general case, the original TAG cannot be considered as a TIG and therefore converted into a strongly equivalent CFG. However, an over-generating TIG can be trivially extracted from the TAG. Parsing with the corresponding CFG, using if necessary the techniques described in this chapter, provides an efficient guide to the TAG parser, in the sense of Boullier (2003).
- 2.
We may say that the canonical form of the empty reduced grammar is \((\{S\}, \emptyset, \emptyset, S)\) though the axiom S does not appear in any production.
- 3.
- 4.
Instead of the classical definition without ε-transitions, we have chosen this definition for compatibility with our definition of ε-free DAGs (see Section 12.2.3). This difference in definitions has no impact on non-empty strings.
- 5.
We may say that the canonical form of the empty reduced FSA is \((\{q_0\}, \emptyset, \emptyset, q_0, \emptyset)\) though the initial state q 0 does not appear in any transition.
- 6.
This is particularly relevant in contexts such as speech processing, lexical ambiguity representation, ambiguous spelling correction, and others.
- 7.
This constraint is not included in the usual definition of DAGs, but it does not decrease their expressive power. It has some drawbacks that we shall not discuss here, but allows us to generalize usual parsing algorithms to DAGs with virtually no effort, as described in the remainder of this section.
- 8.
Where “ε-free” is to be understood according to the definition given above; if ε is in the language, the transition \((1,\varepsilon,f)\) is in δ.
- 9.
It can be shown that the previous check can be performed on \((G^c, w)\) in worst-case time \({\cal O} (|G^c| \times |\varSigma|^3)\) (recall that \(|\varSigma| \leq n\)). This time reduces to \({\cal O} (|G^c| \times |\varSigma|^2)\) if the input sentence is not a DAG but a string.
- 10.
This is equivalent to assuming the existence in the grammar of a super-production whose right-hand side has the form $ S $ .
- 11.
This statement no longer holds if we exclude from P c the productions that have been previously erased during the current a-filter. In that case, an empty set indicates that the production \(Z \rightarrow \alpha U \beta\) can be erased.
- 12.
The homepage of Syntax is http://syntax.gforge.inria.fr/. Syntax is freely available at http://gforge.inria.fr/projects/syntax
- 13.
The name \(G^{T>N}\) comes from this construction process: the set T of terminal symbols of the original grammar has been turned into a subset of the non-terminal symbols N.
- 14.
We use classes of sentences for smoothing purposes: they tackle the sparse data problem that arises when computing medians over sets of sentences of the same length. Indeed, given the modest size of the corpus we used, there are not so many sentences with a same given length, especially for large lengths.
- 15.
As already defined in Section 12.2.1, the size of a CFG is the number of (terminal or non-terminal) symbol occurrences in the set of all productions of the grammar. For example, a grammar made up of n binary rules has size 3n.
- 16.
As seen above, inflected forms are directly terminal symbols of \(G^{T>N}\), while \(G^{TIG}\) uses a lexicon to map these inflected forms into its own terminal symbols, thereby possibly introducing lexical ambiguity.
- 17.
The measures presented in this section have been taken on a 1.7 GHz AMD Athlon PC with 1.5 Gb of RAM running Linux. All parsers are written in C and have been compiled with gcc 2.96 with the O2 optimization flag.
- 18.
Contrarily to classical Earley parsers, its predictor phase uses a pre-computed structure which is roughly an LC relation. Note that this feature forces our filters to compute an LC relation on the generated sub-grammar. This also shows that LC parsers may also benefit from our filtering techniques.
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Boullier, P., Sagot, B. (2010). Are Very Large Context-Free Grammars Tractable?. In: Bunt, H., Merlo, P., Nivre, J. (eds) Trends in Parsing Technology. Text, Speech and Language Technology, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9352-3_12
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