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On input semigroups of automata

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Abstract

In this paper, we consider the problem of what topological semigroups can serve as input semigroups of what (topological) automata. A semigroup is said to be admissible if it serves as an input semigroup of a non-trivial “strongly connected” automaton that has a distinguishable state (see Definition 2). For the discrete or the compact case, the class of all the admissible semigroups is fully characterized: a discrete or compact topological semigroup (I, m) is admissible if and only if there exists a closed congruence relationR such that the quotient semigroup (I/R, m R ) is non-trivial, right simple, and left unital. This work stems from Weeg's [10], who considered a similar problem in the discrete case.

In the last section of the paper, a conjecture of Weeg [10, p. 264] is resolved in the negative.

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References

  1. A. R. Bednarek andA. D. Wallace, Finite approximants of compact totally disconnected machines,Math. Systems Theory 1 (1967), 209–216.

    Google Scholar 

  2. A. R. Bednarek andA. D. Wallace, A relation-theoretic results with applications in topological algebra,Math. Systems Theory 1 (1967), 217–224.

    Google Scholar 

  3. A. H. Clifford, A system arising from a weakened set of group postulates,Ann. of Math. 34 (1933), 865–871.

    Google Scholar 

  4. A. C. Fleck, Structure preserving properties of certain class of functions on automata, Computer Laboratory, Mich. State Univ., May 1961.

  5. A. C. Fleck, Isomorphism groups of automata,J. Assoc. Comput. Mach. 9 (1962), 469–476.

    Google Scholar 

  6. K. H. Hofmann andP. S. Mostert,Elements of compact semigroups, Charles E. Merrill Books, Inc., Columbus, Ohio, 1966.

    Google Scholar 

  7. S. T. Hu,Elements of general topology, Holden-Day, Inc., San Francisco, Calif., 1964.

    Google Scholar 

  8. T. Husain,Introduction to topological groups, W. B. Saunders Co., Philadelphia and London, 1966.

    Google Scholar 

  9. Y.-F. Lin, The structure of not necessarily perfect automata and their auteomorphism groups I,Hung-ching Chow Sixty-fifth Anniversary Volume, Math. Research Center Nat. Taiwan Univ., Taipei (1967), 62–71.

    Google Scholar 

  10. G. P. Weeg, The group and semigroup associated with automata,Proc. Symp. Math. Theory of Automata, New York (1962), 257–266.

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  1. University of South Florida, Tampa, Florida, USA

    Y. -F. Lin

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  1. Y. -F. Lin
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Lin, Y.F. On input semigroups of automata. Math. Systems Theory 4, 35–39 (1970). https://doi.org/10.1007/BF01705883

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  • DOI: https://doi.org/10.1007/BF01705883

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