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New Nonterminal Complexity Results for Semi-conditional Grammars

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Sailing Routes in the World of Computation (CiE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

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Abstract

A semi-conditional grammar is a form of regulated rewriting system. Each rule consists of a context-free core rule \(A\rightarrow w\) and two strings \(w_+,w_-\); the rule is applicable if \(w_+\) (the positive condition) occurs as a substring of the current sentential form, but \(w_-\) (the negative condition) does not. The maximum lengths i, j of the positive or negative conditional strings, respectively, give a natural measure of descriptional complexity, known as the degree of such grammars. Employing several normal form results on phrase-structure grammars as derived by Geffert, we improve on previously obtained results by reducing the number of nonterminals of semi-conditional grammars of a given degree (i, j) while maintaining computational completeness of the said mechanisms.

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Notes

  1. 1.

    We collect all rules \(S\rightarrow w\) with \(S\notin sub (w)\) plus the only rule \(S\rightarrow uS\) within \(P_{cf}\).

  2. 2.

    Some details are suppressed due to space constraints.

References

  1. Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory: EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (1989)

    Book  Google Scholar 

  2. Fernau, H., Freund, R., Oswald, M., Reinhardt, K.: Refining the nonterminal complexity of graph-controlled, programmed, and matrix grammars. J. Autom. Lang. Comb. 12(1/2), 117–138 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Geffert, V.: Normal forms for phrase-structure grammars. RAIRO Informatique théorique et Applications/Theor. Inform. Appl. 25, 473–498 (1991)

    Article  MathSciNet  Google Scholar 

  4. Masopust, T.: Formal models: regulation and reduction. Ph.D. thesis, Faculty of Information Technology, Brno University of Technology, Brno, Czech Republic (2007)

    Google Scholar 

  5. Masopust, T.: A note on the generative power of some simple variants of context-free grammars regulated by context conditions. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 554–565. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00982-2_47

    Chapter  Google Scholar 

  6. Masopust, T., Meduna, A.: Descriptional complexity of semi-conditional grammars. Inf. Process. Lett. 104(1), 29–31 (2007)

    Article  MathSciNet  Google Scholar 

  7. Mayer, O.: Some restrictive devices for context-free languages. Inf. Control (now Inf. Comput.) 20, 69–92 (1972)

    Article  Google Scholar 

  8. Okubo, F.: A note on the descriptional complexity of semi-conditional grammars. Inf. Process. Lett. 110(1), 36–40 (2009)

    Article  MathSciNet  Google Scholar 

  9. Vaszil, G.: On the descriptional complexity of some rewriting mechanisms regulated by context conditions. Theor. Comput. Sci. 330, 361–373 (2005)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. CIRT, Fachbereich 4, Universität Trier, 54286, Trier, Germany

    Henning Fernau

  2. School of Computer Science and Engineering, VIT, Vellore, 632 014, India

    Lakshmanan Kuppusamy

  3. Department of Computer Science, University of Ilorin, P.M.B.1515, Ilorin, Nigeria

    Rufus O. Oladele

Authors
  1. Henning Fernau
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  2. Lakshmanan Kuppusamy
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  3. Rufus O. Oladele
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Corresponding author

Correspondence to Henning Fernau .

Editor information

Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Fernau, H., Kuppusamy, L., Oladele, R.O. (2018). New Nonterminal Complexity Results for Semi-conditional Grammars. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_18

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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