Advertisement

Languages recognized by finite aperiodic groupoids

Extended abstract
  • Martin Beaudry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)

Abstract

We study the context-free languages recognized by a groupoid G in terms of the algebraic properties of the multiplication monoid M(G) of G. Concentrating on the case where M(G) is group-free, we show that all regular languages can be recognized by groupoids for which M(G) is J-trivial and that all groupoids for which M(G) belongs to the larger variety DA recognize only regular languages. Further, we give an example of a groupoid such that M(G) is in the smallest variety outside of DA, and which recognizes all context-free languages not containing the empty word.

Keywords

Regular Language Finite Automaton Empty Word Nondeterministic Finite Automaton Syntactic Monoid 
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. [1]
    M. Beaudry, P. McKenzie and D. Thérien, The membership problem in aperiodic transformation monoids, J. of the Association for Computing Machinery39 (1992), pp. 599–616.Google Scholar
  2. [2]
    F. Bédard, F. Lemieux and P. McKenzie, Extensions to Barrington's M-program model, Theoretical Computer Science (Algorithms, automata, complexity and games)107 (1993), pp. 31–61.Google Scholar
  3. [3]
    H.Caussinus and F.Lemieux, The Complexity of Computing over Quasigroups, Proc. FST& TCS (1994), pp. 36–47.Google Scholar
  4. [4]
    S. Greibach, The Hardest Context-Free Language, SIAM J. on Computing2 (1973), pp. 304–310.CrossRefGoogle Scholar
  5. [5]
    J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley (1979).Google Scholar
  6. [6]
    G. Lallement, Semigroups and Combinatorial Applications, Addison-Wesley (1979).Google Scholar
  7. [7]
    H. Pflugfelder, Quasigroups and Loops: Introduction, Heldermann (1990).Google Scholar
  8. [8]
    J.-E. Pin, Variétés de langages formels, Masson (1984).Google Scholar
  9. [9]
    J. Stern, Complexity of some problems from the theory of automata, Information and Computation66 (1985), pp. 163–176.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Martin Beaudry
    • 1
  1. 1.Département de mathématiques et d'informatiqueUniversité de SherbrookeSherbrookeCanada

Personalised recommendations