An algebraic framework for the study of the syntactic monoids application to the group languages

  • J. Sakarovitch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 45)


We study here a category whose objects are the pairs (M,P) where M is a monoid and P a subset of M. This gives a suitable algebraic framework for studying the relationships between the properties of a language and those of its syntactic monoid, specially in the case of the infinite syntactic monoids as we did in [12, 13, 14]. Some results of Anisimov [1] can be improved within this framework.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ANISIMOV A.V. Sur les langages à groupes (en russe), Kibernetika, Kiev, 1971, no4, 18–24; trad. anglaise in Cybernetics.Google Scholar
  2. [2]
    ANISIMOV A.V. Languages over free groups, in MFCS'75, Lecture Notes in Computer Science no32, Springer Verlag, 1975, 167–171.Google Scholar
  3. [3]
    ANISIMOV A.V. and SEIFERT F.D., Zur algebraischen Charakteristik der durch kontext-freie Sprachen definierten Gruppen, E.I.K. 11, 1975, 695–702.Google Scholar
  4. [4]
    BOASSON L. On the largest full sub-AFL of the full AFL of Context-Free Languages, in MFCS'75, Lecture Notes in Computer Science no 32, Springer Verlag, 1975, 194–198.Google Scholar
  5. [5]
    EILENBERG S. Automata languages and machines, Vol. B, to appear.Google Scholar
  6. [6]
    GINSBURG S. Algebraic and automata-theoretic properties of formal languages, North Holland, 1975.Google Scholar
  7. [7]
    GIVE'ON Y. On some properties of free monoids with applications to automata theory, J. of Comput. and System Sci. 1, 1967, 137–154.Google Scholar
  8. [8]
    KROHN K.B. et RHODES J.L. Algebraic theory of Machines I, Trans. Amer. Math. Soc. 116, 1965, 450–464.Google Scholar
  9. [9]
    MAGNUS W. Residually finite groups, Bull. Amer. Math. Soc., 75, 1969, p. 305–316.Google Scholar
  10. [10]
    NIVAT M. Transductions des languages de Chomsky, Ann. Inst. Fourier, Grenoble, 18, 1968, 339–456.Google Scholar
  11. [11]
    PERROT J-F. Monoïdes syntactiques des langages algébriques, to appear in Acta Informatica.Google Scholar
  12. [12]
    PERROT J-F. et J. SAKAROVITCH Langages algébriques déterministes et groupes abéliens, in Automata Theory and Formal Languages 2nd GI Conference, Lecture notes in Computer Science 33, Springer Verlag, 1975, 20–30.Google Scholar
  13. [13]
    SAKAROVITCH J. Monoïdes syntactiques et langages algébriques, Thèse 3e cycle Math. Univ. Paris VII, 1976.Google Scholar
  14. [14]
    SAKAROVITCH J. Sur les monoïdes syntactiques des langages algébriques déterministes, communication to the III rd International Colloquium on Automata, Languages and Programming, Edinburgh 1976, to appear in Lecture Notes in Computer Science, Springer Verlag.Google Scholar
  15. [15]
    SCHUTZENBERGER M.P. On finite monoids having only trivial subgroup, Information and control 8, 1965, 190–194.CrossRefGoogle Scholar
  16. [16]
    TEISSIER M. Sur les équivalences régulières dans les demi-groupes, C.R. Acad. Sci. Paris, 232, (1951), 1987–1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • J. Sakarovitch
    • 1
  1. 1.Institut de ProgrammationC.N.R.S.France

Personalised recommendations