Abstract
In this chapter we present results which are of interest also for the possible use of contextual grammars in the study of natural language. We start with the basic conditions of the mild context-sensitivity: semilinearity and polynomial parsing. Related to the complexity of parsing are the descriptional complexity and the recognition by means of automata. Ambiguity and structure of strings are other topics important from a linguistic point of view. Part of the investigations here have a preliminary character. Especially complexity, automata recognition, and structuring the phrases are research topics which need further efforts.
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Bibliographical Notes
Theorem 7.3 is from [36]. Section 7.2 is based on [75]. The complexity of languages generated by a special type of internal contextual grammars with finite choice is investigated in [73] (the selector used at a derivation step should overlap the context used at the previous step; again polynomial time algorithms suffice). Section 7.3 is based on [148] and [168]. Related results can be found in [47], [48]. For instance, [47] considers several syntactic complexity measures for contextual grammars with erased contexts (it mainly deals with questions of connectedness), whereas [48] gives decidability results about measures Ax, MAx, TAx, Con, MCon, TCon, Phi for internal contextual grammars (as usual, all measures except Phi are computable for grammars, but for all measures all other computability and decidability problems have negative answers). The automata considered in Section 7.4 are new, but related to certain automata introduced in [160], using the model of contraction automata in [222], as well as the restarting automata in [84]. A particular family of contextual languages is characterized in [82], using these restarting automata. The recent paper [83] considers total contextual grammars with selectors of the form (S L , S M , S R ), with S L , S M , S R regular languages, selecting x 1, x 2, x 3, respectively, in a derivation step x 1 x 2 x 3 ⇒ x 1 ux 2 vx 3. The languages generated in this way are characterized by so-called deleting-restarting automata. Particular cases also cover internal or external contextual families. The ambiguity of external contextual grammars is investigated in [160]. The first assertion in Theorem 7.19 is based on [55]. The ambiguity variants for internal contextual grammars considered in Section 7.5 were introduced in [117]; all results presented here are from [117], except Theorem 7.27, which is from [71]. Section 7.6 is based on [118].
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© 1997 Springer Science+Business Media Dordrecht
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Păun, G. (1997). Linguistically Relevant Properties. In: Marcus Contextual Grammars. Studies in Linguistics and Philosophy, vol 67. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8969-7_7
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DOI: https://doi.org/10.1007/978-94-015-8969-7_7
Publisher Name: Springer, Dordrecht
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