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Implementing Computations in Automaton (Semi)groups

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Implementation and Application of Automata (CIAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7381))

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Abstract

We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order of finite automaton (semi)groups.

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References

  1. Aho, A., Hopcroft, J., Ullman, J.: The Design and Analysis of Computer Algorithms. Addison-Wesley (1974)

    Google Scholar 

  2. Akhavi, A., Klimann, I., Lombardy, S., Mairesse, J., Picantin, M.: On the finiteness problem for automaton (semi)groups. Internat. J. Algebra Comput. (accepted, 2012), arXiv:cs.FL/1105.4725

    Google Scholar 

  3. Antonenko, A.S.: On transition functions of Mealy automata of finite growth. Matematychni Studii 29(1), 3–17 (2008)

    MathSciNet  MATH  Google Scholar 

  4. Bartholdi, L.: FR Functionally recursive groups — a GAP package, v.1.2.4.2 (2011), http://www.uni-math.gwdg.de/laurent/FR/

  5. Bartholdi, L., Reznykov, I.I., Sushchanskiĭ, V.I.: The smallest Mealy automaton of intermediate growth. J. Algebra 295(2), 387–414 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bondarenko, I.V., Bondarenko, N.V., Sidki, S.N., Zapata, F.R.: On the conjugacy problem for finite-state automorphisms of regular rooted trees, ArXiv:math.GR/1011.2227

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. The GAP Group: GAP – Groups, Algorithms, and Programming, v.4.4.12 (2008), http://www.gap-system.org

  9. Grigorchuk, R.I.: On Burnside’s problem on periodic groups. Funktsional. Anal. i Prilozhen. 14(1), 53–54 (1980)

    MathSciNet  Google Scholar 

  10. Grigorchuk, R.I., Nekrashevich, V.V., Sushchanskiĭ, V.I.: Automata, dynamical systems, and groups. Tr. Mat. Inst. Steklova 231, 134–214 (2000)

    MathSciNet  Google Scholar 

  11. Muntyan, Y., Savchuk, D.: automgrp Automata Groups — a GAP package, v.1.1.4.1 (2008), http://finautom.sourceforge.net/

  12. Nekrashevych, V.: Self-similar groups. Mathematical Surveys and Monographs, vol. 117. American Mathematical Society, Providence (2005)

    Google Scholar 

  13. Savchuk, D.M., Vorobets, Y.: Automata generating free products of groups of order 2. J. Algebra 336(1), 53–66 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sidki, S.N.: Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity. J. Math. Sci. (New York) 100(1), 1925–1943 (2000), algebra, 12

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Šuniḱ, Z., Ventura, E.: The conjugacy problem is not solvable in automaton groups (2010), arXiv:math.GR/1010.1993

    Google Scholar 

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Author information

Authors and Affiliations

  1. Sorbonne Paris Cité, LIAFA, UMR 7089 CNRS, Univ Paris Diderot, Paris, France

    Ines Klimann, Jean Mairesse & Matthieu Picantin

Authors
  1. Ines Klimann
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  2. Jean Mairesse
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  3. Matthieu Picantin
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Editor information

Editors and Affiliations

  1. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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© 2012 Springer-Verlag Berlin Heidelberg

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Klimann, I., Mairesse, J., Picantin, M. (2012). Implementing Computations in Automaton (Semi)groups. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_21

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  • DOI: https://doi.org/10.1007/978-3-642-31606-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31605-0

  • Online ISBN: 978-3-642-31606-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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