Advertisement

Hotz-isomorphism theorems in formal language theory

  • Volker Diekert
  • Axel Möbus
Contributed Papers Formal Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)

Abstract

A language \(L \subseteq X*\)is called a language with a Hotz-isomorphism if there is a generating grammar such that its Hotz group is canonically isomorphic to F(X)/L. The main result of the paper states that L is a language with a Hotz-isomorphism if and only if F(X)/L is a finitely presentable group. We also prove an analogous result for Hotz-monoids. Further, we show when the construction of a grammar which allows the Hotz-isomorphism is effective; and we prove various undecidability results concerning this construction.

Keywords

Homomorphic Image Computable Function Surjective Homomorphism Formal Language Theory Monoid Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ClPr67]
    Clifford, A., Preston, G.: The algebraic theory of semigroups, Amer. Math. Soc, vol. I:1961, vol. II:1967Google Scholar
  2. [Diek 85]
    Diekert, V.: On Hotz-groups and homomorphic images of sentential form languages. In: Proc. of the 2nd Annual Symp. on Theoret. Aspects of Comp. Sci., Saarbrücken, January 3–5, 1985. Ed. K. Mehlhorn, Lect. Notes in Comp. Sci. 182 (1985), 87–97Google Scholar
  3. [Diek 86a]
    Diekert, V.: Investigations on Hotz-groups for arbitrary grammars, Acta Informatica 22 (1986), 679–698Google Scholar
  4. [Diek 86b]
    Diekert, V.: On some variants of the Ehrenfeucht conjecture, Theoret.Comp. Sci. 46 (1986), 313–318Google Scholar
  5. [FrSV 82]
    Frougny, C., Sakarovitch, J., Valkema, E.: On the Hotz-group of a context-free grammar, Acta Informatica 18 (1982), 109–115Google Scholar
  6. [Hotz 80]
    Hotz, G.: Eine neue Invariante für kontext-freie Sprachen, Theoret. Comp. Sci. 11 (1980), 107–116Google Scholar
  7. [HoUl 79]
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation, Addison-Wesley: Massachusetts 1979Google Scholar
  8. [Möbus 86]
    Möbus, A.: On languages with a Hotz-isomorphism (Manuscript 1986)Google Scholar
  9. [Serre 65]
    Serre, J.P: Cohomologie galoisienne, Lect.Notes in Math. 5, Springer: 1965Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Volker Diekert
    • 1
  • Axel Möbus
    • 2
  1. 1.Institut für Informatik der Technischen Universität MünchenMünchen 2
  2. 2.Mathematisches Institut der Universität DüsseldorfDüsseldorf

Personalised recommendations