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Maximal dense intervals of grammar forms

  • Valtteri Niemi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

The existence of maximal dense intervals of grammar forms is shown, and an explicit example of such an interval is given. It is shown to be decidable whether or not two given context-free grammars make up a maximal dense interval. The results are based on a construction that builds a new language from subsets of a given language. Directed graphs are studied as an application.

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References

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    H. A. Maurer, A. Salomaa and D. Wood, Dense hierarchies of grammatical families Journal of the ACM 29 (1982), 118–126.Google Scholar
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    H. A. Maurer, A. Salomaa, E. Welzl and D. Wood, Denseness, maximality and decidability of grammatical families, Ann. Acad. Scient. Fennicae 11 (1986), 167–178.Google Scholar
  3. [3]
    V. Niemi, Density of grammar forms (Parts I and II), Intern. Journal of Computer Mathematics 20 (1986), 3–21 and 91–114.Google Scholar
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    E. Welzl, Color-families are dense, Theoretical Computer Science 17 (1982), 29–42.Google Scholar
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    D. Wood, Grammar and L Forms: An Introduction, Springer-Verlag Lecture Notes in Comp. Science No. 91, New York, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Valtteri Niemi
    • 1
  1. 1.Mathematics DepartmentUniversity of TurkuTurkuFinland

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