Even Linear Simple Matrix Languages: Formal Language Aspects

  • Henning Fernau
Conference paper
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Abstract

We investigate formal language properties of even linear simple matrix languages and related language classes. More precisely, we discuss characterizations, (proper) inclusion relations, closure properties and decidability questions. In another paper [4], we showed the importance of these language classes for grammatical inference issues.

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References

  1. 1.
    J. Berstel. Transductions and Context-Free Languages. Stuttgart: Teubner, 1979.MATHGoogle Scholar
  2. 2.
    J. A. Brzozowski. Regular-like expressions for some irregular languages. In 9th IEEE SWAT (FOCS), pages 278–280, 1968.Google Scholar
  3. 3.
    J. Dassow and Gh. Păun. Regulated Rewriting in Formal Language Theory, vol. 18 of EATCS Monographs in Theoretical Computer Science. Berlin: Springer, 1989.Google Scholar
  4. 4.
    H. Fernau. Efficient learning of some linear matrix languages. In 5th COCOON, vol. 1627 of LNCS, pages 221–230, 1999. Extended version as Technical Report WSI-2000–9, Universität Tübingen (Germany), Wilhelm-Schickard-Institut für Informatik.Google Scholar
  5. 5.
    H. Fernau and J. M. Sempere. Permutations and control sets for learning non-regular language families. In 5th ICGI, vol. 1891 of LNCS/LNAI, pages 75–88, 2000.Google Scholar
  6. 6.
    S. Ginsburg and E. H. Spanier. Control sets on grammars. Mathematical Systems Theory, 2: 159–177, 1968.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    S. Greibach. Comments on universal and left universal grammars, context-sensitive languages, and context-free grammar forms. Information and Control, 39: 135–142, 1978.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    S. Hirose and M. Nasu. Left universal context-free grammars and homomorphic characterizations of languages. Information and Control, 50: 110–118, 1981.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    N. A. Khabbaz. A geometric hierarchy of languages. Journal of Computer and System Sciences, 8: 142–157, 1974.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    E. Mäkinen. A note on the grammatical inference problem for even linear languages. Fundamenta Informaticae, 25: 175–181, 1996.MathSciNetMATHGoogle Scholar
  11. 11.
    C. Martín-Vide. Natural language understanding: a new challenge for grammar systems. Acta Cybernetica, 12: 461–472, 1996.MATHGoogle Scholar
  12. 12.
    A. Mateescu. Special families of matrix languages and decidable problems. Acta Cybernetica, 10: 45–52, 1991.MathSciNetMATHGoogle Scholar
  13. 13.
    H. Maurer and W. Kuich. Tuple languages. In Proc. of the ACM International Computing Symposium, pages 882–891, 1970.Google Scholar
  14. 14.
    Gh. Păun. Linear simple matrix languages. Elektronische Informationsverarbeitung and Kybernetik (EIK), 14: 377–384, 1978.MATHGoogle Scholar
  15. 15.
    J. M. Sempere and P. García. A characterization of even linear languages and its application to the learning problem. In 2nd ICGI, vol. 862 of LNCS/LNAI, pages 38–44, 1994.Google Scholar
  16. 16.
    R. Siromoney. On equal matrix languages. Information and Control, 14: 133–151, 1969.CrossRefGoogle Scholar
  17. 17.
    Y. Takada. Grammatical inference of even linear languages based on control sets. Information Processing Letters, 28: 193–199, 1988.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Y. Takada. Learning even equal matrix languages based on control sets. In ICPIA’92, vol. 652 of LNCS, pages 274–289, 1992.Google Scholar
  19. 19.
    Y. Takada. A hierarchy of language families learnable by regular language learning. Information and Computation, 123: 138–145, 1995.MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Y. Takada. Learning formal languages based on control sets. In Algorithmic Learning for Knowledge-Based Systems, vol. 961 of LNCS/LNAI, pages 317–339, 1995.Google Scholar
  21. 21.
    D. J. Weir. A geometric hierarchy beyond context-free languages. Theoretical Computer Science, 104: 235–261, 1992.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Henning Fernau
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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