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Monoïdes syntactiques des langages algébriques

Syntactic monoids of algebraic languages

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Summary

Syntactic monoids have been considered so far almost only for rational (= regular) languages. We start here a systematic study of the syntactic monoids of algebraic (= context-free) languages. We exhibit a whole class of finitely generated monoids, none of which is isomorphic to the syntactic monoid of an algebraic language. We show that if M 1 and M 2 are syntactic monoids of algebraic languages L 1 and L 2, and if neither M 1 nor M 2 has a zero, then there exists an algebraic language L whose syntactic monoid is isomorphic to the direct product M 2×M2. We then prove that the algebraic language ¯L 0 Complement of {n n yn zn; n≧1} has a syntactic monoid M 0 such that M 0×M 0 is not isomorphic to the syntactic monoid of any algebraic language, whence follows that any algebraic language L′ whose syntatic monoid is isomorphic to M 0 must be non deterministic.

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Bibliographie

  1. Allen, Jr., D.: On a characterization of the nonregular set of primes. J. Computer System Sciences 2, 464–467 (1968)

    Google Scholar 

  2. Anisimov, A. V.: Sur les langages à groupe (en russe). Kibernetika (Kiev) n∘ 4, 18–24 (1971); trad. Anglaise: Cybernetics 7, 594–601

    Google Scholar 

  3. Berstel, J.: Memento sur les transductions rationnelles. In: Actes de l'Ecole de Printemps sur les langages algébriques, Bonascre (Ariège), Avril 1973

  4. Boasson, L.: Paires itérantes et Langages Algébriques. Thèse Sc. Math., Univ. Paris VII, 1974

  5. Clifford, A. H., Preston, G. B.: The algebraic theory of semigroups. Providence (R.I.): American Math. Soc., Vol. 1, 1961; Vol. 2, 1967

    Google Scholar 

  6. Ginsburg, S.: The mathematical theory of context-free languages. New York: McGraw-Hill 1966

    Google Scholar 

  7. Maurer, H. A.: The solution of a problem by Ginsburg. Information Processing Letters 1, 7–10 (1971)

    Google Scholar 

  8. McNaughton, R., Papert, S.: Counter-free automata. Cambridge (Mass.): M.I.T. Press 1971

    Google Scholar 

  9. Nivat, M., Perrot, J-F.: Une généralisation du monoïde bicyclique. C.R. Acad. Sci. Paris Sér. A 271, 824–827 (1970)

    Google Scholar 

  10. Ogden, W.: A helpful result for proving inherent ambiguity. Math. Systems Theory 2, 191–194 (1967)

    Google Scholar 

  11. Perrin, D.: Codes bipréfixes et groupes de permutations. Thèse Sc. Math., Univ. Paris VII, 1975

  12. Perrot, J-F.: Sur la fermeture commutative des C-langages. C.R. Acad. Sci. Paris 265, 597–600 (1967)

    Google Scholar 

  13. Perrot, J-F.: Une famille de monoïdes 0-bisimples généralisant le monoïde bicyclique. Séminaire Dubreil (Algèbre), Paris, 1971/72, exposé n∘ 3

  14. Perrot, J-F.: Contribution à l'étude des monoïdes syntactiques et de certains groupes associés aux automates finis. Thèse Sc. Math., Univ. Paris VI, 1972

  15. Perrot, J-F.: Groupes de permutations associés aux codes préfixes finis. In: A. Lentin (ed.), Permutations. Actes du Colloque, Paris 1972. Paris: Gauthier-Villars 1974, pp. 19–35

    Google Scholar 

  16. Perrot, J-F.: Syntaktische Monoide gewisser kontext-freier Sprachen. A paraître dans les Seminarberichte der GMD, Bonn

  17. Perrot, J-F., Sakarovitch, J.: Langages algébriques déterministes et groupes abéliens. In: Automata Theory and Formal Languages, 2nd G.I. Conference. Lecture Notes in Computer Science 33. Berlin-Heidelberg-New York: Springer 1975, p. 20–30

  18. Redei, L.: Die Verallgemeinerung der Schreierschen Erweiterungstheorie. Acta Scientia Mathematica 14, 252–273 (1952)

    Google Scholar 

  19. Sakarovitch, J.: Monoïdes syntactiques et langages algébriques. Thèse de 3e cycle, Univ. Paris VII, 1976

  20. Schein, B. M.: Homomorphisms and subdirect decompositions of semigroups. Pacific J. Mathematics 17, 529–547 (1966)

    Google Scholar 

  21. Schützenberger, M. P.: Une théorie algébrique du codage. Séminaire Dubreil-Pisot (Algèbre et théorie des nombres), Paris, 1955/56, exposé n∘ 15

  22. Schützenberger, M. P.: Sur certaines variétés de monoïdes finis. In: E. R. Caianiello (ed.), Automata theory. London-New York : Academic Press 1966, pp. 314–319

    Google Scholar 

  23. Schützenberger, M. P.: Sur les monoïdes finis dont les groupes sont commutatifs. Rev. Française Automat. Informat. Recherche Operationelle R-1 55–61 (1974)

    Google Scholar 

  24. Valkema, E.: Zur Charakterisierung formaler Sprachen durch Halbgruppen. Dissertation, Kiel, 1974

  25. Zalcstein, Y.: Syntactic semigroups of somme classes of star-free languages. In: M. Nivat (ed.), Automata, Languages, and Programming. Amsterdam: North-Holland 1973, p. 135–144

    Google Scholar 

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  1. Institut de Programmation, Université Paris VI, 2, Place Jussieu, F-75230, Paris Cedex 05, France

    J. -F. Perrot

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Perrot, J.F. Monoïdes syntactiques des langages algébriques. Acta Informatica 7, 399–413 (1977). https://doi.org/10.1007/BF00289471

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