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A descriptive characterisation of linear languages

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Abstract

Lautemann et al. (1995) gave a descriptive characterisation of the class of context-free languages, showing that a language is context-free iff it is definable as the set of words satisfying some sentence of a particular logic (fragment) over words. The present notes discuss how to specialise this result to the class of linear languages. Somewhat surprisingly, what would seem the most straightforward specialisation actually fails, due to the fact that linear grammars fail to admit a Greibach normal form. We identify an alternative specialisation, based on an alternative characterisation of context-free languages, also noted by Lautemann et al. (1995).

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References

  • Amar, V., & Putzolu, G. (1964). On a family of linear grammars. Information and Control, 7, 283–291.

    Article  Google Scholar 

  • Eiter, T., Gottlob, G., & Gurevich, Y. (2000). Existential second-order logic over strings. Journal of the ACM, 47, 77–131.

    Article  Google Scholar 

  • Gécseg, F., & Steinby, M. (1997). Tree languages. In Rozenberg, G. and A. Salomaa, editors, Handbook of Formal Languages, vol. 3, Springer-Verlag.

  • Greibach, S. (1965). A new normal-form theorem for context-free phrase structure grammars. Journal of the ACM, 12, 42–52.

    Article  Google Scholar 

  • Hopcroft, J.E., & Ullman, J.D. (1979). Introduction to Automata Theory, Languages, and Computation. Addison–Wesley.

  • Langholm, T., & Bezem, M. (2003). A descriptive characterisation of even linear languages. Grammars 6, 169–181.

    Article  Google Scholar 

  • Lautemann, C., Schwentick, T., & Thérien, D. (1995). Logics for context-free languages. In Pacholsky, L. and J. Tiuryn, editors, Computer Science Logic, LNCS 933, 205–216. Springer-Verlag.

  • Rosenkrantz, D.J. (1967). Matrix equations and normal forms for context-free grammars. Journal of the ACM, 14, 501–507.

    Article  Google Scholar 

  • Thomas, W. (1997). Languages, Automata and Logic. In Rozenberg, G. and A. Salomaa, editors, Handbook of Formal Languages, Vol. 3, Springer-Verlag.

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  1. Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316, Oslo, Norway

    Tore Langholm

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  1. Tore Langholm
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Correspondence to Tore Langholm.

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Langholm, T. A descriptive characterisation of linear languages. JoLLI 15, 233–250 (2006). https://doi.org/10.1007/s10849-006-9016-z

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  • DOI: https://doi.org/10.1007/s10849-006-9016-z

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