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Monoids described by pushdown automata

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Aspects and Prospects of Theoretical Computer Science (IMYCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 464))

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Abstract

We define and study a family of monoids, called (PR)-monoids, of rather low complexity. A (PR)-monoid is a monoid the multiplication of which may be realized by a deterministic pushdown automaton. We prove that this family contains rational monoids, free groups and is closed under finitely generated submonoids and free products. We also consider other families of monoids of the same complexity than (PR)-monoids.

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References

  1. Benois M. (1969), “Parties rationnelles du groupe libre”, C.R. Acad. Sci. Paris, Ser. A 269, 1188–1190.

    Google Scholar 

  2. Berstel J. (1979), “Transductions and Context-free Languages”, Teubner, Stuttgart.

    Google Scholar 

  3. Choffrut Ch. (1978), “Contribution à l'étude de quelques familles remarquables de fonctions rationnelles”, Thèse Sci. math., Univ. Paris 6, Paris.

    Google Scholar 

  4. Eilenberg S. (1974), “Automata, Languages and Machines”, Vol. A, Academic Press, New York.

    Google Scholar 

  5. Fliess M. (1971), “Deux applications de la représentation matricielle d'une série rationnelle non commutative”, Journal of Algebra, 19, 344–353.

    Article  Google Scholar 

  6. Ginsburg S. (1966), “The Mathematical Theory of Context-free Languages”, Mac Graw Hill.

    Google Scholar 

  7. Ginsburg S., Greibach S. (1966), “Deterministic Context-free Languages”, Inform. and Control, 9, 620–648.

    Google Scholar 

  8. Nivat M. (1968), “Transductions des langages de Chomsky”, Ann. Inst. Fourier, 18, 339–456.

    Google Scholar 

  9. Nivat M. (1970), “Sur les automates à mémoire à pile”, Proc. of International Computing Symposium, Bonn (W. Itzfeld, ed.); North Holland, 655–663.

    Google Scholar 

  10. Pelletier M. (1989), “Descriptions de semigroupes par automates”, Thèse de l'Université Paris 6.

    Google Scholar 

  11. Sakarovitch J. (1979), “Syntaxe des langages de Chomsky”, Th. Sc. Math., Univ. Paris 7.

    Google Scholar 

  12. Sakarovitch J. (1981), “Description des monoïdes de type fini”, EIK, 17, 417–434.

    Google Scholar 

  13. Sakarovitch J. (1987), Easy Multiplications. I. The Realm of Kleene's Theorem, Information and Computation, Vol. 74, No. 3, 173–197.

    Google Scholar 

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Authors and Affiliations

  1. LITP, Université Paris 6, 4 Place Jussieu, 75230, Paris Cedex 05, France

    Maryse Pelletier

Authors
  1. Maryse Pelletier
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Jürgen Dassow Jozef Kelemen

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© 1990 Springer-Verlag Berlin Heidelberg

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Pelletier, M. (1990). Monoids described by pushdown automata. In: Dassow, J., Kelemen, J. (eds) Aspects and Prospects of Theoretical Computer Science. IMYCS 1990. Lecture Notes in Computer Science, vol 464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53414-8_42

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  • DOI: https://doi.org/10.1007/3-540-53414-8_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53414-3

  • Online ISBN: 978-3-540-46869-1

  • eBook Packages: Springer Book Archive

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