Sur une propriété d'itération des langages algébriques déterministes


The aim of this paper is to establish an iterative property for deterministic context-free languages. This property then allows one to infer the nondeterminism of context-free languages of a certain family from the structure of their syntactic monoids.

This is a preview of subscription content, log in to check access.


  1. 1.

    H. Alt et K. Mehlhorn, Lower bounds for the space complexity of context-free recognition, in3 rd International Colloquium on Automata, Languages and Programming (S. Michaelson and R. Milner, Eds.) Edinburgh University Press, 338–354, 1976.

  2. 2.

    L. Boasson, Two iteration theorems for some families of languages,J. of Comput. and System Sci. 7, 583–596, 1973.

    Google Scholar 

  3. 3.

    L. Boasson, Langages algébriques, paires itérantes et transductions rationnelles,Theoretical Computer Sci. 2, 209–223, 1976.

    Google Scholar 

  4. 4.

    J. A. Brzozowski et I. Simon, Characterizations of locally testable events,Discrete Mathematics 4, 243–271, 1973.

    Google Scholar 

  5. 5.

    A. H. Clifford et G. B. Preston,The Algebraic Theory of Semigroups, American Math. Soc. Vol. 1, 1961, Vol. 2, 1967.

  6. 6.

    B. Courcelle, Applications de la théorie des langages à la théorie des schémas de programmes, Thèse 3ème cycle math., Univ. Paris 7, 1974.

  7. 7.

    S. Eilenberg,Automata, langages and machines, Vol. B, Academic Press, 1976.

  8. 8.

    S. Ginsburg,The mathematical theory of context-free languages, McGraw-Hill, 1966.

  9. 9.

    S. Ginsburg et S. Greibach, Deterministic context-free languages,Inf. and Control 9, 620–648, 1966.

    Google Scholar 

  10. 10.

    M. A. Harrison et I. M. Havel, Strict deterministic grammars,J. of Comput. and System Sci. 7, 237–277, 1973.

    Google Scholar 

  11. 11.

    M. A. Harrison et I. M. Havel, On the parsing of deterministic languages,J. Assoc. Computing Machinery 21, 525–548, 1974.

    Google Scholar 

  12. 12.

    S. Lang,Algebra, Addison Wesley, 1965.

  13. 13.

    R. McNaughton et S. Papert,Counter-free Automata, Cambridge: MIT Press, 1971.

    Google Scholar 

  14. 14.

    M. Nivat, Transductions des langages de Chomsky,Ann. Inst. Fourier, 18, Grenoble, 339–456, 1968.

    Google Scholar 

  15. 15.

    W. Ogden, A helpful result for proving inherent ambiguity,Math. System Theory 2, 191–194, 1967.

    Google Scholar 

  16. 16.

    W. Ogden, Intercalation theorems for pushdown store and stack languages, Ph.D. Thesis, Stanford, 1968.

  17. 17.

    D. Perrin, La transitivité du groupe d'un code bipréfixe fini,Math. Zeitschrift, 153, 283–287, 1977.

    Google Scholar 

  18. 18.

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

  19. 19.

    J-F. Perrot, Monoïdes syntactiques des langages algébriques,Acta Informatica, 7, 399–413, 1977.

    Google Scholar 

  20. 20.

    J-F. Perrot et J. Sakarovitch, Langages algébriques déterministes et groupes abéliens, inAutomata Theory and Formal Languages 2nd GI Conference, Lecture notes in Computer Science 33, Springer Verlag, 20–30.

  21. 21.

    J-F. Perrot et J. Sakarovitch, A theory of syntactic monoïds for context-free languages, inInformation Processing 77, (B. Gilchrist Ed.), North Holland, 1977, 69–72.

  22. 22.

    J. Sakarovitch, Monoïdes syntactiques et langages algébriques, Thèse 3ème cycle math., Univ. Paris VII, Paris, 1976.

    Google Scholar 

  23. 23.

    J. Sakarovitch, Sur les monoides syntactiques des langages algébriques déterministes, in3 rd International Colloquium on Automata, Languages and Programming (S. Michaelson and R. Milner, Eds.), Edinburgh University Press, 1976, pp. 52–65.

  24. 24.

    J. Sakarovitch, On deterministic commutative context-free language, inProceedings of a Conference on Theoretical Computer Science held at Waterloo, Ontario, Canada (E. Ashroft and J. Brzozowski, Eds.), 88–93, 1977.

  25. 25.

    J. Sakarovitch, Monoïdes pointés,Semigroup Forum 18, 235–264 (1979).

    Google Scholar 

  26. 26.

    M. P. Schützenberger, Une théorie algébrique du codage, Séminaire Dubreil-Pisot, année 1955–56, exposé n° 15.

  27. 27.

    M. P. Schützenberger, On finite monoids having only trivial subgroups,Information and Control 8, 190–194, 1965.

    Google Scholar 

  28. 28.

    I. Simon, Piecewise testable events, inAutomata theory and formal languages, 2nd GI Conference, Lecture Notes in Computer Science 33, Springer-Verlag, 214–222.

  29. 29.

    J. Smith, Monoid acceptors and their relation to formal languages, Ph.D. Thesis, University of Pennsylvania, 1972.

  30. 30.

    R. E. Stearns, A regularity test for pushdown machines,Information and Control 11, 323–340, 1967.

    Google Scholar 

  31. 31.

    M. Teissier, Sur les équivalences régulières dans les demi-groupes,C. R. Acad. Sci. Paris, 232, 1987–1989, (1951).

    Google Scholar 

  32. 32.

    L. G. Valiant, Decision procedures for families of deterministic pushdown automata, Ph.D. Dissert., Univ. of Warwick, Coventry, 1973.

  33. 33.

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

  34. 34.

    Y. Zalcstein, Syntactic semigroups of some classes of star-free languages, inAutomata, Languages and Programming (M. Nivat, Ed.), North-Holland, 1973, 135–144.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sakarovitch, J. Sur une propriété d'itération des langages algébriques déterministes. Math. Systems Theory 14, 247–288 (1981).

Download citation