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The family of one-counter languages is closed under quotient

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Summary

We study, first, the operation of quotient in connection with rational transductions. We show, afterwards, that Rocl, the family of one counter languages is closed under quotient by a context-free language. On the contrary, every recursively enumerable language is the quotient of two linear languages.

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References

  1. Autebert, J.M.: Non-principalité du cylindre des langages à compteurs. Math. Syst. Theory 11, 157–167 (1977)

    Google Scholar 

  2. Baker, B.S., Book, R.V.: Reversal-bounded Multipushdown Machines. J. Comput. Syst. Sci. 8, 315–332 (1974)

    Google Scholar 

  3. Beauquier, J.: Independence of linear and one-counter generators. In: Fundamentals of Computation Theory, pp. 45–51. Berlin: Akademie 1979

    Google Scholar 

  4. Berstel, J.: Transductions and context-free languages. Stuttgart: Teubner 1979

    Google Scholar 

  5. Boasson, L.: Two Iteration theorems for some families of languages. J. Comput. Syst. Sci. 7, 583–596 (1973)

    Google Scholar 

  6. Book, R.V., Jantzen, M., Wrathall, C.: Monadic Thue Systems. Theor. Comput. Sci. 19, 231–251 (1982)

    Google Scholar 

  7. Ginsburg, S.: Algebraic and Automata-Theoretic properties of Formal Languages. Amsterdam: North-Holland 1975

    Google Scholar 

  8. Greibach, S.: One-counter languages and the IRS condition. J. Comput. Syst. Sci. 10, 237–247 (1975)

    Google Scholar 

  9. Greibach, S.: A note on the recognition of one-counter languages. RAIRO, Inf. Theor. R2, 5–12 (1975)

    Google Scholar 

  10. Greibach, S.: Remarks on blind and partially blind one-way multi-counter machines. Theor. Comput. Sci. 7, 311–324 (1978)

    Google Scholar 

  11. Greibach, S.: One-counter languages and the chevron operation. RAIRO, Inf. Theor. 13, 189–194 (1979)

    Google Scholar 

  12. Harrison, M.A.: Introduction to Formal Language Theory. Reading, MA.: Addison Wesley 1978

    Google Scholar 

  13. Jantzen, M.: On the hierarchy of Petri Net languages. RAIRO, Inf. Theor. 13, 19–30 (1979)

    Google Scholar 

  14. Jantzen, M.: The power of synchronizing operations on strings. Theor. Comput. Sci. 14, 127–154 (1981)

    Google Scholar 

  15. Latteux, M.: Langages commutatifs. Thesis, Lille 1, 1978

  16. Latteux, M.: Langages à un compteur. J. Comput. Syst. Sci. 26, 14–33 (1983)

    Google Scholar 

  17. Latteux, M., Rozenberg, G.: Commutative one-counter languages are regular. J. Comput. Syst. Sci. 29, 54–57 (1984)

    Google Scholar 

  18. Nivat, M.: Transductions des langages de Chomsky. Ann. Inst. Fourier, Grenoble 18, 339–455 (1967)

    Google Scholar 

  19. Ratoandromanana, B.: Ordre et quotient dans les familles de langages algébriques. Thesis, University of Lille 1, 1984

  20. Turakainen, P.: On characterization of recursively enumerable languages in terms of linear languages and VW-grammars. Proc. K. Ned. Akad. Wet., Amsterdam 81, 145–153 (1978)

    Google Scholar 

  21. Yntema, M.K.: Inclusion relations among families of context-free languages. Inf. Control 10, 572–597 (1967)

    Google Scholar 

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Authors and Affiliations

  1. U.E.R. I.E.E.A., Informatique, CNRS, LA 369, Université de Lille I, F-59655, Villeneuve d'Ascq, France

    M. Latteux, B. Leguy & B. Ratoandromanana

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  1. M. Latteux
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  2. B. Leguy
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  3. B. Ratoandromanana
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Latteux, M., Leguy, B. & Ratoandromanana, B. The family of one-counter languages is closed under quotient. Acta Informatica 22, 579–588 (1985). https://doi.org/10.1007/BF00267045

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