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The characterization of parallel ultralinear grammars by rational power series

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Summary

Given a reduced context-free grammar G, the following statements are equivalent:

  1. (i)

    G is parallel ultralinear,

  2. (ii)

    G is parallel nonterminal bounded,

  3. (iii)

    PL(G), the parallel label language, is regular,

  4. (iv)

    f G(y, z), the generating function counting height and length of the yield of the derivation trees of G, is rational.

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References

  1. Altman, E., Banerji, R.: Some problems of finite representability. Information and Control 8, 251–263 (1965)

    Google Scholar 

  2. Fleck, A.C.: An analysis of grammars by their derivation sets. Information and Control 24, 389–398 (1974)

    Google Scholar 

  3. Ginsburg, S., Spanier, E.H.: Finite-turn pushdown automata. SIAM J. Control 4, 429–453 (1966)

    Google Scholar 

  4. Kuich, W.: On the entropy of context-free languages. Information and Control 16, 173–200 (1970)

    Google Scholar 

  5. Kuich, W., Prodinger, H., Urbanek, F.J.: On the height of derivation trees. In: Automata, Languages and Programming (H.A. Maurer, ed.). Lecture Notes in Computer Science, Vol. 71. pp. 370–384. Berlin-Heidelberg-New York: Springer, 1979

    Google Scholar 

  6. Moriya, E.: Associate languages and derivational complexity of formal grammars and languages. Information and Control 22, 139–162 (1973)

    Google Scholar 

  7. Rozenberg, G., Vermeir, D.: Extending the notion of finite index. In: Automata, Languages, and Programming (H.A. Maurer, ed.). Lecture Notes in Computer Science, Vol. 71; pp. 479–488. Berlin-Heidelberg-New York: Springer, 1979

    Google Scholar 

  8. Salomaa, A.: Formal languages. New York: Academic Press, 1973

    Google Scholar 

  9. Salomaa, A., Soittola, M.: Automata — theoretic aspects of formal power series, Springer, 1979

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Authors and Affiliations

  1. Institut für Mathematische Logik und Formale Sprachen, Technische Universität Wien, Wien, Austria

    Werner Kuich

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  1. Werner Kuich
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Kuich, W. The characterization of parallel ultralinear grammars by rational power series. Acta Informatica 15, 129–139 (1981). https://doi.org/10.1007/BF00288960

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  • DOI: https://doi.org/10.1007/BF00288960

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