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Asian Conference on Intelligent Information and Database Systems

ACIIDS 2014: Intelligent Information and Database Systems pp 53–62Cite as

Nonterminal Complexity of Weakly Conditional Grammars

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8397))

Abstract

A weakly conditional grammar is specified as a pair K = (G, G′) where G is a context-free grammar, and G′ is a regular grammar such that a production rule of G is only applicable to the sentential form if it belongs to the language generated by G′. The nonterminal complexity Var(K) of the grammar K is defined as the sum of the numbers of nonterminals of G and G′. This paper studies the nonterminal complexity of weakly conditional grammars, and it proves that every recursively enumerable language can be generated by a weakly conditional grammar with no more than ten nonterminals. Moreover, it shows that the number of nonterminals in such grammars without erasing rules leads to an infinite hierarchy of families of languages generated by weakly conditional grammars.

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References

  1. Friś, J.: Grammars with partial ordering of rules. Information and Control 12, 415–425 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  2. Salomaa, A.: Formal languages. Academic press, New York (1973)

    Google Scholar 

  3. Kelemen, J.: Conditional grammars: Motivations, definitions, and some properties. In: Proc. Conf. Automata, Languages and Mathematical Sciences, pp. 110–123 (1984)

    Google Scholar 

  4. Meduna, A.: Generalized forbidding grammars. International Journal of Computer Mathematics 36(1-2), 31–38 (1990)

    Article  MATH  Google Scholar 

  5. Meduna, A., Gopalaratnam, A.: On semi-conditional grammars with productions having either forbidding or permitting conditions. Acta Cybernetica 11(4), 307–323 (1994)

    MATH  MathSciNet  Google Scholar 

  6. Navratil, E.: Context-free grammars with regular conditions. Kybernetika 2, 118–126 (1970)

    MathSciNet  Google Scholar 

  7. Pǎun, G.: A variant of random context grammars: Semi-conditional grammars. Theoretical Computer Science 41, 1–17 (1985)

    Article  MathSciNet  Google Scholar 

  8. Král, J.: A note on grammars with regular restrictions. Kybernetika 9(3), 159–161 (1973)

    MATH  MathSciNet  Google Scholar 

  9. Pǎun, G.: On the generative capacity of conditional grammars. Information and Control 43, 178–186 (1979)

    Article  MathSciNet  Google Scholar 

  10. Meduna, A., Švec, M.: Reduction of simple semi-conditional grammars with respect to the number of conditional productions. Acta Cybernetica 15, 353–360 (2002)

    MATH  MathSciNet  Google Scholar 

  11. Meduna, A., Švec, M.: Descriptional complexity of generalized forbidding grammars. International Journal of Computer Mathematics 80(1), 11–17 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Vaszil, G.: On the descriptional complexity of some rewriting mechanisms regulated by context conditions. Theoretical Computer Science 330, 361–373 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Turaev, S., Dassow, J., Manea, F., Selamat, M.: Language classes generated by tree controlled grammars with bounded nonterminal complexity. Theoretical Computer Science 449, 134–144 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  14. Turaev, S., Dassow, J., Selamat, M.H.: Language classes generated by tree controlled grammars with bounded nonterminal complexity. In: Holzer, M., Kurtib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 289–300. Springer, Heidelberg (2011)

    Google Scholar 

  15. Turaev, S., Dassow, J., Selamat, M.: Nonterminal complexity of tree controlled grammars. Theoretical Computer Science 412, 5789–5795 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Dassow, J., Pǎun, G.: Regulated rewriting in formal language theory. Springer, Berlin (1989)

    Book  Google Scholar 

  17. Rozenberg, G., Salomaa, A. (eds.): Handbook of formal languages, pp. 1–3. Springer (1997)

    Google Scholar 

  18. Geffert, V.: Context-free-like forms for phrase-structure grammars. In: Chytil, M.P., Koubek, V., Janiga, L. (eds.) MFCS 1988. LNCS, vol. 324, pp. 309–317. Springer, Heidelberg (1988)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100, Kuala Lumpur, Malaysia

    Sherzod Turaev & Norsaremah Salleh

  2. Department of Information Systems , Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100, Kuala Lumpur, Malaysia

    Mohd Izzuddin Mohd Tamrin

Authors
  1. Sherzod Turaev
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  2. Mohd Izzuddin Mohd Tamrin
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  3. Norsaremah Salleh
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Ngoc Thanh Nguyen  & Bogdan Trawiński  & 

  2. Faculty of Engineering, Department of Computer Engineering, King Mongkut’s Institute of Technology Ladkrabang, 10520, Bangkok, Thailand

    Boonwat Attachoo

  3. Software Engineering Program, King Mongkut’s Institute of Technology Ladkrabang, 10520, Bangkok, Thailand

    Kulwadee Somboonviwat

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© 2014 Springer International Publishing Switzerland

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Turaev, S., Mohd Tamrin, M.I., Salleh, N. (2014). Nonterminal Complexity of Weakly Conditional Grammars. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds) Intelligent Information and Database Systems. ACIIDS 2014. Lecture Notes in Computer Science(), vol 8397. Springer, Cham. https://doi.org/10.1007/978-3-319-05476-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-05476-6_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05475-9

  • Online ISBN: 978-3-319-05476-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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