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Grammar systems as language analyzers and recursively enumerable languages

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

We consider parallel communicating grammar systems which consist of several grammars and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such grammar systems with context-free productions and present characterizations of the family of recursively enumerable languages by them.

In accepting parallel communicating grammar systems rules of the form α → A with a word α and a nonterminal A are applied as in the generating case, and the language consists of all terminal words which can derive the axiom. We prove that all types of these accepting grammar systems describe the family of recursively enumerable languages, even if Λ-rules are forbidden.

Moreover, we study analyzing parallel communicating grammar systems, the derivations of which perform the generating counterparts backwards. This requires a modication of the generating derivation concept to strong-returning parallel communicating grammar systems which also generate the family of recursively enumerable languages.

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Author information

Authors and Affiliations

  1. Fakultä at für Informatik, Otto-von-Guericke-Universitä at Magdeburg, PSF 4120, D-39016, Magdeburg, Germany

    Henning Bordihn & Júrgen Dassow

  2. Hungarian Academy of Sciences, Computer and Automation Research Institute, Kende u. 13 - 17, H-1111, Budapest, Hungary

    Gyorgy Vaszil

Authors
  1. Henning Bordihn
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  2. Júrgen Dassow
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  3. Gyorgy Vaszil
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Bordihn, H., Dassow, J., Vaszil, G. (1999). Grammar systems as language analyzers and recursively enumerable languages. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_10

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  • DOI: https://doi.org/10.1007/3-540-48321-7_10

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  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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