@InProceedings{KLI,
  author ={Ines Klimann},
  title ={{The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable}},
  booktitle ={30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages ={502--513},
  series ={Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN ={978-3-939897-50-7},
  ISSN ={1868-8969},
  year ={2013},
  volume ={20},
  editor ={Natacha Portier and Thomas Wilke},
  publisher ={Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address ={Dagstuhl, Germany},
  URL ={http://drops.dagstuhl.de/opus/volltexte/2013/3960},
  URN ={urn:nbn:de:0030-drops-39605},
  doi ={http://dx.doi.org/10.4230/LIPIcs.STACS.2013.502},
  annote ={Keywords: Mealy automata, automaton semigroups, decidability of finiteness, decidability of freeness, Nerode equivalence}
}


@article {AKL,
    AUTHOR = {Akhavi, Ali and Klimann, Ines and Lombardy, Sylvain and
              Mairesse, Jean and Picantin, Matthieu},
     TITLE = {On the finiteness problem for automaton (semi)groups},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {22},
      YEAR = {2012},
    NUMBER = {6},
     PAGES = {1250052, 26},
      ISSN = {0218-1967},
   MRCLASS = {20F10 (20E08 20M35)},
  MRNUMBER = {2974106},
       DOI = {10.1142/S021819671250052X},
       URL = {http://dx.doi.org/10.1142/S021819671250052X},
}

@incollection {GSESS,
    AUTHOR = {Rostislav Grigorchuk and Dmytro Savchuk},
     TITLE = {Self-similar groups acting essentially freely on the boundary of the binary rooted tree},
 BOOKTITLE = {Group Theory, Combinatorics, and Computing},
    SERIES = {Contemp. Math.},
    VOLUME = {611},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2014},
}


@BOOK{harpe,
  key       = "H00",
  author    = "P. de la Harpe",
  title     = "Topics in geometric group theory",
  series    = "Chicago Lectures in Mathematics",
  publisher = "{The University of Chicago Press}",
  year      = 2000,
}

@article {BKNV05,
    AUTHOR = {Laurent Bartholdi and Vadim Kaimanovich and Volodymyr
Nekrashevych},
     TITLE = {On amenability of automata groups},
   JOURNAL = {Duke Mathematical Journal},
    VOLUME = {154},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {575--598},
}

@article {Sid00,
    AUTHOR = {Sidki, Said},
     TITLE = {Automorphisms of one-rooted trees: growth, circuit structure,
              and acyclicity},
   JOURNAL = {J. Math. Sci. (New York)},
  FJOURNAL = {Journal of Mathematical Sciences (New York)},
    VOLUME = {100},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {1925--1943},
      ISSN = {1072-3374},
     CODEN = {JMTSEW},
   MRCLASS = {05C25 (05C45 68Q45)},
  MRNUMBER = {MR1774362 (2002g:05100)},
}


@article {GNS00,
AUTHOR = {Grigorchuk, R. I. and Nekrashevich, V. V. and
              Sushchanski{\u\i}, V. I.},
     TITLE = {Automata, dynamical systems, and groups},
   JOURNAL = {Tr. Mat. Inst. Steklova},
  FJOURNAL = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova.
              Rossi\u\i skaya Akademiya Nauk},
    VOLUME = {231},
      YEAR = {2000},
    NUMBER = {Din. Sist., Avtom. i Beskon. Gruppy},
     PAGES = {134--214},
      ISSN = {0371-9685},
   MRCLASS = {37B15 (20F10 68Q45 68Q70)},
  MRNUMBER = {MR1841755 (2002m:37016)},
}

@preamble{
   "\def\cprime{$'$} "
}
@article {Gri80,
    AUTHOR = {Grigor{\v{c}}uk, R. I.},
     TITLE = {On {B}urnside's problem on periodic groups},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u\i\ Analiz i ego
              Prilozheniya},
    VOLUME = {14},
      YEAR = {1980},
    NUMBER = {1},
     PAGES = {53--54},
      ISSN = {0374-1990},
   MRCLASS = {20F05},
  MRNUMBER = {MR565099 (81m:20045)},
MRREVIEWER = {N. S. Chernikov},
}

@article {GZ02a,
    AUTHOR = {Grigorchuk, Rostislav I. and Zuk, Andrzej},
     TITLE = {On a torsion-free weakly branch group defined by a three state
              automaton},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {12},
      YEAR = {2002},
    NUMBER = {1-2},
     PAGES = {223--246},
      ISSN = {0218-1967},
   MRCLASS = {20F69 (20E08 68Q70)},
  MRNUMBER = {MR1902367 (2003c:20048)},
MRREVIEWER = {Laurent Bartholdi},
}

@incollection {GZ02b,
    AUTHOR = {Grigorchuk, Rostislav I. and Zuk, Andrzej},
     TITLE = {Spectral properties of a torsion-free weakly branch group
              defined by a three state automaton},
 BOOKTITLE = {Computational and statistical group theory (Las Vegas,
              NV/Hoboken, NJ, 2001)},
    SERIES = {Contemp. Math.},
    VOLUME = {298},
     PAGES = {57--82},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2002},
   MRCLASS = {60B15 (20E08 20M35 60G50 68Q70)},
  MRNUMBER = {MR1929716 (2003h:60011)},
MRREVIEWER = {Michael Voit},
}

@article {BV05,
    AUTHOR = {Bartholdi, Laurent and Vir{\'a}g, B{\'a}lint},
     TITLE = {Amenability via random walks},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {130},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {39--56},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {43A07 (20P05 60G50)},
  MRNUMBER = {MR2176547 (2006h:43001)},
MRREVIEWER = {Vydas {\v{C}}ekanavi{\v{c}}ius},
      NOTE = {(available at http://arxiv.org/abs/math.GR/0305262)},
}

@incollection {BP06,
    AUTHOR = {Bux, Kai-Uwe and P{\'e}rez, Rodrigo},
     TITLE = {On the growth of iterated monodromy groups},
 BOOKTITLE = {Topological and asymptotic aspects of group theory},
    SERIES = {Contemp. Math.},
    VOLUME = {394},
     PAGES = {61--76},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2006},
   MRCLASS = {20F65 (20E08 37F20 37F50)},
  MRNUMBER = {MR2216706 (2006m:20062)},
MRREVIEWER = {Laurent Bartholdi},
      NOTE = {(available at http://www.arxiv.org/abs/math.GR/0405456)},
}

@article {BS07,
    AUTHOR = {Bondarenko, Ievgen V. and Savchuk, Dmytro M.},
     TITLE = {On {S}ushchansky {$p$}-groups},
   JOURNAL = {Algebra Discrete Math.},
  FJOURNAL = {Algebra and Discrete Mathematics},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {22--42},
      ISSN = {1726-3255},
   MRCLASS = {20F50 (20E08)},
  MRNUMBER = {MR2364061},
}


@article{GSS07,
    AUTHOR = {Grigorchuk, Rostislav and Savchuk, Dmytro and {\v{S}}uni{\'c}, Zoran},
    TITLE  = {The spectral problem, substitutions and iterated monodromy},
   JOURNAL = {CRM Proceedings and Lecture Notes},
    VOLUME = {42},
      YEAR = {2007},
    NUMBER = {8},
     PAGES = {225--248},
}

@article {GS06a,
    AUTHOR = {Grigorchuk, Rostislav and {\v{S}}uni{\'k}, Zoran},
     TITLE = {Asymptotic aspects of {S}chreier graphs and {H}anoi {T}owers
              groups},
   JOURNAL = {C. R. Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {342},
      YEAR = {2006},
    NUMBER = {8},
     PAGES = {545--550},
      ISSN = {1631-073X},
   MRCLASS = {20E08},
  MRNUMBER = {MR2217913},
}

@incollection {GS06b,
    AUTHOR = {Grigorchuk, Rostislav and {\v{S}}uni{\'c}, Zoran},
     TITLE = {Schreier spectrum of the {H}anoi {T}owers group on three pegs},
 BOOKTITLE = {Analysis on graphs and its applications},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {77},
     PAGES = {183--198},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2008},
   MRCLASS = {91A43 (05C25 05C50 20E08 28Axx)},
  MRNUMBER = {MR2459869},
}


@article {BN06,
    AUTHOR = {Bartholdi, Laurent I. and Nekrashevych, Volodymyr V.},
     TITLE = {Thurston equivalence of topological polynomials},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {197},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {1--51},
      ISSN = {0001-5962},
}

@ARTICLE{Sus79,
  author  = "V. I. Sushchansky",
  title   = "Periodic permutation $p$-groups and the unrestricted  {Burnside} problem",
  journal = "DAN SSSR.",
  volume  = 247,
  number  = 3,
  pages   = "557--562",
  year    = 1979,
  note    = "(in Russian)",
}

@incollection {Gri05,
    AUTHOR = {Grigorchuk, Rostislav},
     TITLE = {Solved and unsolved problems around one group},
 BOOKTITLE = {Infinite groups: geometric, combinatorial and dynamical
              aspects},
    SERIES = {Progr. Math.},
    VOLUME = {248},
     PAGES = {117--218},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2005},
   MRCLASS = {20-02 (20Exx 20Fxx)},
  MRNUMBER = {MR2195454},
}

@article {GLSZ00,
    AUTHOR = {Grigorchuk, Rostislav I. and Linnell, Peter and Schick, Thomas
              and Zuk, Andrzej},
     TITLE = {On a question of {A}tiyah},
   JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
              Math\'ematique},
    VOLUME = {331},
      YEAR = {2000},
    NUMBER = {9},
     PAGES = {663--668},
      ISSN = {0764-4442},
     CODEN = {CASMEI},
   MRCLASS = {57R20 (46L99 46N99)},
  MRNUMBER = {MR1797748 (2001m:57050)},
}

@article {Ale83,
    AUTHOR = {Aleshin, S. V.},
     TITLE = {A free group of finite automata},
   JOURNAL = {Vestnik Moskov. Univ. Ser. I Mat. Mekh.},
  FJOURNAL = {Vestnik Moskovskogo Universiteta. Seriya I. Matematika,
              Mekhanika},
      YEAR = {1983},
    NUMBER = {4},
     PAGES = {12--14},
      ISSN = {0201-7385},
   MRCLASS = {68D30 (20E05)},
  MRNUMBER = {MR713968 (84j:68035)},
MRREVIEWER = {Boris M. Schein},
}

@article {VV05,
    AUTHOR = {Vorobets, Mariya and Vorobets, Yaroslav},
     TITLE = {On a free group of transformations defined by an automaton},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {124},
      YEAR = {2007},
     PAGES = {237--249},
      ISSN = {0046-5755},
     CODEN = {GEMDAT},
   MRCLASS = {20E05 (20E08)},
  MRNUMBER = {MR2318547},
}



@article {BGK32,
    AUTHOR = {Bondarenko, I. and Grigorchuk, R. and Kravchenko, R. and Muntyan, Y. and Nekrashevych, V.
 and Savchuk, D. and \v{S}uni\'{c}, Z.},
     TITLE = {Classification of groups generated by $3$-state automata over $2$-letter alphabet},
   JOURNAL = {Algebra Discrete Math.},
  FJOURNAL = {Algebra and Discrete Mathematics},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--163},
      ISSN = {1726-3255},
   MRCLASS = {20F50 (20E08)},
}


@article {BGK06,
    AUTHOR = {Bondarenko, I. and Grigorchuk, R. and Kravchenko, R. and Muntyan, Y. and Nekrashevych, V.
 and Savchuk, D. and \v{S}uni\'{c}, Z.},
     TITLE = {Groups generated by $3$-state automata over a $2$-letter alphabet, {I}},
   JOURNAL = {S\~ao Paulo Journal of Mathematical Sciences},
      YEAR = {2007},
    VOLUME = {1},
    NUMBER = {1},
     PAGES = {1--40},
      NOTE = {(available at \emph{http://arxiv.org/abs/math.GR/0612178})},
   MRCLASS = {20F50 (20E08)},
}



@article {BGK07,
    AUTHOR = {Bondarenko, I. and Grigorchuk, R. and Kravchenko, R. and
              Muntyan, Y. and Nekrashevych, V. and Savchuk, D. and
              {\v{S}}uni{\'c}, Z.},
     TITLE = {Groups generated by 3-state automata over a 2-letter alphabet.
              {II}},
      NOTE = {Functional analysis},
   JOURNAL = {J. Math. Sci. (N. Y.)},
  FJOURNAL = {Journal of Mathematical Sciences (New York)},
    VOLUME = {156},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {187--208},
      ISSN = {1072-3374},
     CODEN = {JMTSEW},
   MRCLASS = {68Q45},
  MRNUMBER = {2760318 (2012e:68194)},
       DOI = {10.1007/s10958-008-9262-5},
       URL = {http://dx.doi.org/10.1007/s10958-008-9262-5},
}


@article{GS83,
    AUTHOR = {Gupta, Narain and Sidki, Sa{\"{\i}}d},
     TITLE = {On the {B}urnside problem for periodic groups},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {182},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {385--388},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {20F50},
  MRNUMBER = {MR696534 (84g:20075)},
MRREVIEWER = {Seymour Bachmuth},
}

@article {FG85,
    AUTHOR = {Fabrykowski, Jacek and Gupta, Narain},
     TITLE = {On groups with sub-exponential growth functions},
   JOURNAL = {J. Indian Math. Soc. (N.S.)},
  FJOURNAL = {The Journal of the Indian Mathematical Society. New Series},
    VOLUME = {49},
      YEAR = {1985},
    NUMBER = {3-4},
     PAGES = {249--256 (1987)},
      ISSN = {0019-5839},
     CODEN = {JIMTA2},
   MRCLASS = {20E99 (20F05 20F19)},
  MRNUMBER = {MR942349 (90e:20029)},
MRREVIEWER = {Martha K. Smith},
}

@article {BG02,
    AUTHOR = {Bartholdi, Laurent and Grigorchuk, Rostislav I.},
     TITLE = {On parabolic subgroups and {H}ecke algebras of some fractal
              groups},
   JOURNAL = {Serdica Math. J.},
  FJOURNAL = {Serdica. Mathematical Journal. Serdika. Matematichesko
              Spisanie},
    VOLUME = {28},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {47--90},
      ISSN = {1310-6600},
   MRCLASS = {20E08 (20C08)},
  MRNUMBER = {MR1899368 (2003c:20027)},
MRREVIEWER = {S. Andreadakis},
}

@article{Ers04,
    AUTHOR = {Erschler, Anna},
     TITLE = {Boundary behavior for groups of subexponential growth},
   JOURNAL = {Annals of Math.},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {160},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {1183--1210},
}

@article {Gri84,
    AUTHOR = {Grigorchuk, R. I.},
     TITLE = {Degrees of growth of finitely generated groups and the theory
              of invariant means},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {48},
      YEAR = {1984},
    NUMBER = {5},
     PAGES = {939--985},
      ISSN = {0373-2436},
   MRCLASS = {20F05 (43A07)},
  MRNUMBER = {MR764305 (86h:20041)},
MRREVIEWER = {P. Gerl},
}

@article {Bar03,
    AUTHOR = {Bartholdi, Laurent},
     TITLE = {A {W}ilson group of non-uniformly exponential growth},
   JOURNAL = {C. R. Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {336},
      YEAR = {2003},
    NUMBER = {7},
     PAGES = {549--554},
      ISSN = {1631-073X},
   MRCLASS = {20F05},
  MRNUMBER = {MR1981466 (2004c:20051)},
MRREVIEWER = {Stephen P. Humphries},
}

@article {Wil04,
    AUTHOR = {Wilson, John S.},
     TITLE = {On exponential growth and uniformly exponential growth for
              groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {155},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {287--303},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {20F05},
  MRNUMBER = {2 031 429},
}

@article {BRS06,
    AUTHOR = {Bartholdi, L. and Reznykov, I. I. and Sushchansky, V. I.},
     TITLE = {The smallest {M}ealy automaton of intermediate growth},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {295},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {387--414},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {68Q45 (20M35 68Q70)},
  MRNUMBER = {MR2194959 (2006i:68060)},
MRREVIEWER = {K. G. Peeva},
}

@article {Nek07,
    AUTHOR = {Nekrashevych, Volodymyr},
     TITLE = {A minimal {C}antor set in the space of 3-generated groups},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {124},
      YEAR = {2007},
     PAGES = {153--190},
      ISSN = {0046-5755},
     CODEN = {GEMDAT},
   MRCLASS = {20F65},
  MRNUMBER = {MR2318543},
}
