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On Context-Sensitive Grammars

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Formal Languages and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 148))

Abstract

This is an overview on context-sensitive grammars. The paper contains also an appendix about Chomsky type-0 grammars (also called phrase-structure grammars). These grammars and families of languages are arising in classical language theory. Most of the topics presented in this paper are in some sense modifications of the classical notion of a rewriting system, introduced by Axel Thue at the beginning of 20th century, [44]. A rewriting system is a (finite) set of rules u → ν, where u and ν are words, indicating that an occurrence of u (as a subword) can be replaced by ν. A rewriting system only transforms words into other words, languages into other languages. After supplementing it with some mechanism for “squeezing out” a language, a rewriting system can be used as a device for defining languages. This is what Chomsky did, with linguistic goals in mind, when he introduced different types of grammars, [3, 4, 5], see also [6]. At the beginning, the classification was not very clear but by mid-60’s the four classes of the Chomsky hierarchy of grammars and languages have become pretty standard: recursively enumerable,or of type 0; context-sensitive, or of type 1; context-free, or of type 2; regular,or of type 3.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania

    Alexandru Mateescu

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  1. Alexandru Mateescu
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Editors and Affiliations

  1. Research Group on Mathematical Lingustics, Rovira i Virgili University, Pl. Imperial Tàrraco 1, 43005, Tarragona, Spain

    Carlos Martín-Vide

  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania

    Victor Mitrana

  3. Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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Mateescu, A. (2004). On Context-Sensitive Grammars. In: Martín-Vide, C., Mitrana, V., Păun, G. (eds) Formal Languages and Applications. Studies in Fuzziness and Soft Computing, vol 148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39886-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-39886-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53554-3

  • Online ISBN: 978-3-540-39886-8

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