Abstract
The minimal and maximal use of selectors are only two possible ideas for modifying the definition of contextual grammars or of the languages generated by them. The following three chapters are devoted to the study of such variants. Many of them correspond to classical ideas explored in formal language theory, especially for context-free grammars, but many others are specific to contextual grammars.
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Bibliographical Notes
Contextual grammars with erased contexts and with one-sided contexts are introduced in [177]. The results in Section 10.1 and those in Theorem 10.4 are from [177]. Theorem 10.5 is from [37] and the diagram in Figure 10.1 is from [39]. Deterministic grammars are first considered in [177]. Theorem 10.10 is from [36]. Leftmost derivations are introduced in [178]; prefix and leftmost maximal derivations are introduced in [181]. The results in Section 10.4 are based on these two papers. The parallel derivation is introduced in [180]; Theorems 10.15 – 10.17 are from [219]. The parallel prefix maximal derivation is investigated in [181]; Theorems 10.18 – 10.20 are from this paper. [28] and [128] consider the maximal parallel derivation without the prefix restriction: in the current string a number of selectors are identified such that in the remaining substrings no selector can be found. The generative capacity and undecidability results similar to those proved here for parallel prefix maximal derivation are proved in [128]. Section 10.6 is based on [180], Section 10.7 is based on [114]. A more restrictive variant of the depth-first derivation is introduced in [73], where the obtained languages are proved to be parsable in polynomial time. External grammars with marked derivations are introduced in [139] (and then investigated in [160]) under the name of v-contextual grammars. Internal contextual grammars with an infinite number of contexts are considered in [166]. Contextual grammars with pattern selectors are introduced and briefly investigated in [112] (Table 10.2 appears there, the other results are new).
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© 1997 Springer Science+Business Media Dordrecht
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Păun, G. (1997). Variants of Contextual Grammars. In: Marcus Contextual Grammars. Studies in Linguistics and Philosophy, vol 67. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8969-7_10
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DOI: https://doi.org/10.1007/978-94-015-8969-7_10
Publisher Name: Springer, Dordrecht
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