Skip to main content
SpringerLink
Log in

On right congruences associated with the input semigroupS of automata

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

LetA=(M, S, δ) be an automaton without outputs whereM is a nonemptyset andS is a nonempty semigroup. Then the right congruences μM and μ m associated withS have been expressed in many different ways (μ M is called the Myhill-Nerode congruence onS). Also, their algebraic properties have been investigated. We have introduced the right congruences μ S and μα onM and we have obtained necessary and sufficient conditions thatS/μ andM/w have nontrivialS-homomorphisms where μ andw are any right congruences onS andM respectively. The faithfulness ofS has been introduced.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fleck, A. C.,Isomorphism groups of automata, J. ACM9 (1962), 469–476.

    Article  MATH  MathSciNet  Google Scholar 

  2. Hoehnke, H. J.,Zur Strukturtheorie der Halbgruppen, Math. Nachr.26 (1963), 1–13.

    MATH  MathSciNet  Google Scholar 

  3. Hoehnke, H. J.,Structure of Semigroups, Canad. J. Math.18 (1966), 449–491.

    MATH  MathSciNet  Google Scholar 

  4. Oehmke, R. H.,The semigroup of a strongly connected automaton, Semigroup Forum15 (1978), 351–356.

    Article  MATH  MathSciNet  Google Scholar 

  5. Oehmke, R. H.,On the structure of an automaton and its input semigroup, J. ACM10 (1963), 521–525.

    Article  MATH  MathSciNet  Google Scholar 

  6. Park, C. H.,The direct product and module-like properties of automata, Ph.D. thesis, University of Iowa, 1989.

  7. Park, C. H.,Algebraic properties associated with the input semigroup S of an automaton, Bull. Korean Math. Soc.27 (1990), 69–83.

    Article  MATH  MathSciNet  Google Scholar 

  8. Tully, E. J.,Representation of a semigroup by transformations acting transitively on set, Amer. J. Math.83 (1961), 533–541.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The SungHwa University-Asan Campus, Cheon An, South Korea

    Chin-Hong Park

Authors
  1. Chin-Hong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. B. McFadden

The author thanks both the editor and the referee for their generous help in revising this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Park, CH. On right congruences associated with the input semigroupS of automata. Semigroup Forum 48, 263–271 (1994). https://doi.org/10.1007/BF02573677

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02573677

Keywords

Search

Navigation