Abstract
This chapter describes the relationship between LA-grammars and LA-parsers in comparison with other systems proposed in the literature. Section 8.1 characterizes the formal relationship between LA-grammar and associated LA-parsers and generators. Section 8.2 gives a formal account of the relation between LA-grammar and finite automata. Section 8.3 describes how LA-grammar differs from recursive-transition networks (RTNs) and augmented-transition networks (ATNs). Section 8.3 compares LA-grammars with Predictive Analyzers and Deterministic Parsers. Section 8.5 compares LA-grammars and Register Machines.
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References
Barton et al., (1987), p. 189.
Or “driver”, in the terminology of LR-parsing. See Aho & Ullman (1979), pp. 197 f.
Berwick & Weinberg (1984), p. 41.
The rule counter is part of the testing environment of LA-grammar, and was written with the help of Todd Kaufmann of Carnegie Mellon University.
For further discussion of LA-grammar complexity see Chapter 10.
This generator for LA-grammar was implemented by Todd Kaufmann.
In another version, ‘gram-gen’ is called with the maximal surface length rather than the recursion factor.
Woods (1970).
After Hopcroft & Ullman (1979), p. 17.
Even though LA-grammar did not evolve from FAs, it may be regarded formally as an extension of FAs. But it constitutes by no means the first formal extension of standard FAs. Rabin and Scott (1959) investigated the decision properties of two-way, two-tape FAs.
See Hopcroft and Ullman (1970), pp. 16–21 for a detailed discussion of this language.
The implementation of 8.2.4 uses the symbol $ to indicate the empty sentence start.
Woods (1970).
Another extension of context-free grammars are “attribute grammars” (Knuth 1969).
Cf. history section 3 of 3.2.2.
See Hausser (1986), Section 4.3., for the analysis of center-embedded relative clauses in German.
Quoted from Kuno and Oettinger (1963).
Though Marcus’ system is only partly data driven. See Marcus 1980, p. 14.
The modified version of Marcus’ parser presented in Berwick (1985) does without rule packets.
Cf. 3.4.4, 3.4.5, 10.4.2, 10.4.3.
This section resulted from several discussions with Helmut Schwichtenberg.
Of course, one may use properties other than “halting” to construct diagonalization arguments in LA-grammar. See Cantor’s diagonalization lemma in Shoenfield (1967), p. 131.
Provided by Helmut Schwichtenberg.
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© 1989 Springer-Verlag Berlin Heidelberg
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Hausser, R. (1989). LA-Grammar and Automata. In: Computation of Language. Symbolic Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74564-5_9
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DOI: https://doi.org/10.1007/978-3-642-74564-5_9
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