Abstract
Section 7.1 presents three theorems which relate types of LA-grammars to the recursive languages in the Chomsky hierarchy. Section 7.2 introduces a new hierarchy, which is more natural for LA-grammar. Section 7.3 explains the notions of non-determinism, syntactic ambiguity, and lexical ambiguity. Section 7.4 discusses an example of a syntactically-ambiguous LA-grammar. Section 7.5 explains the properties of lexically-ambiguous LA-grammars.
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References
See Hopcroft and Ullman (1979) for further discussion.
See Hopcroft and Ullman (1979), p. 79.
See Hopcroft and Ullman (1979), p. 223.
See Hopcroft and Ullman (1979), p. 217.
Hopcroft & Ullman (1979), pp. 107 f.
Hopcroft and Ullman (1979), p. 113.
Hopcroft & Ullman (1979), p. 225.
See Theorem 3 (7.1.1), Theorem 4 (7.1.2), and Theorem 5 (7.1.7) above.
This finite constant will vary between different grammars.
The definition of C-LAGs and B-LAGs benefitted from a discussion with Helmut Schwichtenberg.
The categorial operation of r-3 defines a function because the segment $ is introduced only once (by r-2).
For detailed discussion of finite automata see Section 8.2. The complexity result for unambiguous C-LAGs is given in Section 10.1.
The class of D-LAGs is defined in Section 9.2
Earley doesn’t distinguish between syntactically- and lexically-ambiguous LAGs. His result of n 3 for “ambiguous” context-free grammars holds only for “packed parsing” (cf. Section 10.3).
Cf. Hopcroft and Ullman (1979), Chapter 12. Berwick and Weinberg (1984), p. 149, call non-deterministic systems a “convenient mathematical fiction.”
E.g., the house belongs in the class of singular noun phrases, but not in the class plural noun phrases. Furthermore, the houses belongs in the class of plural noun phrases, but not in the class of singular noun phrases.
See Hopcroft and Ullman (1979), pp. 99 – 103, for a detailed discussion of this language within the PS-grammar paradigm.
The inclusion of at least one unambiguous propositional constant in the lexicon of 3SAT is necessary in order for the propositional variables to be genuinely lexically ambiguous in the sense of definition 7.3.11.
Alternatively, the rules could have been defined to operate only at the beginning of the categories. But then the categories would be intuitively less transparent.
Hopcroft and Ullman, p. 325.
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© 1989 Springer-Verlag Berlin Heidelberg
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Hausser, R. (1989). Language Hierarchies. In: Computation of Language. Symbolic Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74564-5_8
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DOI: https://doi.org/10.1007/978-3-642-74564-5_8
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