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Minimal Covers of Formal Languages

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Developments in Language Theory (DLT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2295))

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Abstract

Let L,L′ be languages. If L ⫅ L′, we say that L′ covers L. Let C,D be two classes of languages. If L′ ∈ C, we say that L′ is a minimal C-cover with respect to D if whenever L ⫅ L″ ⫅ L′ and L″∈ C, we have L′ - L″ ∈ D. In this paper we discuss minimal C-covers with respect to finite languages, when C is the class of regular languages.

Research supported in part by a grant from NSERC.

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References

  1. J. Balcázar, J. Dýaz, and J. Gabarró. Structural Complexity I, volume 11 ofEATCSMonographs on Theoretical Computer Science. Springer-Verlag, 1988.

    Google Scholar 

  2. C. Câmpeanu, N. Sântean and S. Yu. Minimal cover-automata for finite languages. In J.-M. Champarnaud, D. Maurel and D. Ziadi, editors, WIA’ 98, volume 1660 of Lecture Notes in Computer Science, pages 43–56. Springer-Verlag, 1999.

    Google Scholar 

  3. N.J. Fine and H.S. Wilf. Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc., 16:109–114, 1965.

    Google Scholar 

  4. P. Flajolet and J. M. Steyaert. On sets having only hard subsets. In J. Loeckx, editor, Proc. 2nd Colloq. on Automata, Languages and Programming (ICALP), volume 14 of Lecture Notes in Computer Science, pages 446–457. Springer-Verlag, 1974.

    Google Scholar 

  5. S. Ginsburg and E. H. Spanier. Bounded regular sets. Proc. Amer. Math. Soc., 17:1043–1049, 1966.

    Google Scholar 

  6. S. A. Greibach. A note on undecidable properties of formal languages. Math. Systems Theory, 2:1–6, 1968.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.

    Google Scholar 

  8. H. B. Hunt III, D. J. Rosenkrantz and T. G. Szymanski. On the equivalence, containment, and covering problems for the regular and context-free languages. J. Comput. System Sci., 12:222–268, 1976.

    MATH  MathSciNet  Google Scholar 

  9. M. Latteux and G. Thierrin. Semidiscrete context-free languages. Internat. J. Comput. Math. 14(1):3–18, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  10. R.C. Lyndon and M. P. Schützenberger. The equation a M = b N c P in a free group. Michigan Math. J., 9:289–298, 1962.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. L. Post. Recursively enumerable sets of positive integers and their decision problems. Bull. Amer. Math. Soc., 50:284–316, 1944.

    Article  MATH  MathSciNet  Google Scholar 

  12. G. Păun and A. Salomaa. Thin and slender languages. Disc. Appl. Math., 61:257–270, 1995.

    Article  MATH  Google Scholar 

  13. H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing and Information Science, Queen’s University, K7L 3N6, Kingston, Ontario, Canada

    Michael Domaratzki

  2. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Jeffrey Shallit

  3. Department of Computer Science, University of Western Ontario, N6A 3K7, London, Ontario, Canada

    Sheng Yu

Authors
  1. Michael Domaratzki
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  2. Jeffrey Shallit
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  3. Sheng Yu
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Editor information

Editors and Affiliations

  1. Institut für Algebra und Computermathematik Abt. für Theoretische Informatik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Werner Kuich

  2. Department of Computer Science, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkaisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Domaratzki, M., Shallit, J., Yu, S. (2002). Minimal Covers of Formal Languages. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_28

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  • DOI: https://doi.org/10.1007/3-540-46011-X_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43453-5

  • Online ISBN: 978-3-540-46011-4

  • eBook Packages: Springer Book Archive

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