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Self-automaton semigroups

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Abstract

After reviewing automaton semigroups, we introduce Cayley automata and the corresponding Cayley automaton semigroups. We investigate which semigroups are isomorphic to their Cayley automaton semigroup and give some results for special classes of semigroups. We answer a question posed by Cain relating to the dual construction.

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References

  1. Arbib, M., Krohn, K., Rhodes, J.: Algebraic Theory of Machines, Languages and Semigroups. Academic Press, New York (1968)

    MATH  Google Scholar 

  2. Cain, A.J.: Automaton semigroups. Theor. Comput. Sci. 410, 5022–5038 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Krohn, K., Rhodes, J.: Algebraic theory of machines I: prime decomposition theorem for finite semigroups and machines. Trans. Am. Math. Soc. 116, 450–464 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  4. Mintz, A.: On the Cayley semigroup of a finite aperiodic semigroup. Int. J. Algebr. Comput. 19(6), 723–746 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Maltcev, V.: Cayley automaton semigroups. Int. J. Algebr. Comput. 19(1), 79–95 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Silva, P.V., Steinberg, B.: On a class of automata groups generalizing lamplighter groups. Int. J. Algebr. Comput. 15(5–6), 1213–1234 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Steinberg, B.: Existence of a possible counterexample in automaton semigroups, http://mathoverflow.net/questions/134694 (2013). Accessed 28 June 2013

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Acknowledgments

The author is extremely grateful to Nik Ruškuc and Collin Bleak for their many helpful contributions and valuable discussions whilst this work was being undertaken.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews , KY16 9SS, UK

    Alexander McLeman

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  1. Alexander McLeman
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Correspondence to Alexander McLeman.

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Communicated by Benjamin Steinberg.

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McLeman, A. Self-automaton semigroups. Semigroup Forum 90, 189–206 (2015). https://doi.org/10.1007/s00233-014-9610-3

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  • DOI: https://doi.org/10.1007/s00233-014-9610-3

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