Representations of a free group of rank two by time-varying Mealy automata
Discussiones Mathematicae - General Algebra and Applications (2005)
- Volume: 25, Issue: 1, page 119-134
- ISSN: 1509-9415
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topAdam Woryna. "Representations of a free group of rank two by time-varying Mealy automata." Discussiones Mathematicae - General Algebra and Applications 25.1 (2005): 119-134. <http://eudml.org/doc/287683>.
@article{AdamWoryna2005,
abstract = {In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.},
author = {Adam Woryna},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {changing alphabet; Mealy automaton; time-varying automaton; group generated by time-varying automaton; free group; representations of free groups; time-varying Mealy automata},
language = {eng},
number = {1},
pages = {119-134},
title = {Representations of a free group of rank two by time-varying Mealy automata},
url = {http://eudml.org/doc/287683},
volume = {25},
year = {2005},
}
TY - JOUR
AU - Adam Woryna
TI - Representations of a free group of rank two by time-varying Mealy automata
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2005
VL - 25
IS - 1
SP - 119
EP - 134
AB - In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.
LA - eng
KW - changing alphabet; Mealy automaton; time-varying automaton; group generated by time-varying automaton; free group; representations of free groups; time-varying Mealy automata
UR - http://eudml.org/doc/287683
ER -
References
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- [2] L. Bartholdi, R.I. Grigorchuk and V. Nekrashevych, From fractal groups to fractal sets, 'Fractals in Graz 2001', Birkhäuser, Basel 2003, 25-118. Zbl1037.20040
- [3] R.I. Grigorchuk, V. V. Nekrashevich and V.I. Sushchanskii, Automata, Dynamical Systems and Groups, Proc. Steklov Inst. Math. 231 (2000), 128-203. Zbl1155.37311
- [4] R.I. Grigorchuk and A. Żuk, Lectures on Automata Groups, Dynamics on Tress, and L2-invariants, 'Advanced Course on Automata Groups' (July 5-16, 2004 at CRM), Centre de Recerca Matemàtica, Universitat Autonòma de Barcelona, Bellaterra, Spain, (preprint, 2004).
- [5] A. Olijnyk, Free products of C2 as groups of finitely automatic permutations, (in Russian), Voprosy Algebry 14 (1999), 158-165.
- [6] A.S. Olijnyk and V.I. Sushchanskii, Free Groups of Infinitely Unitriangular Matrices, Math. Notes 67 (2000), 320-324.
- [7] V.I. Sushchanskii, Group of Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1998, no. 6, 47-51.
- [8] V.I. Sushchanskii, Group of Finite Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1999, no. 2, 48-52.
- [9] A. Woryna, On transformations given by time-varying Mealy automata, (Polish), Zeszyty Nauk. Politech. Śląskiej, no. 1581, Ser. Automatyka 138 (2003), 201-215.
- [10] A. Woryna, On the group permutations generated by time-varying Mealy automata, Publ. Math. Debrecen, 67 (2005), 115-130. Zbl1081.20042
- [11] A. Woryna, On representation of a semidirect product of cyclic groups by a 2-state time-varying Mealy automaton, Zeszyty Nauk. Politech. Śląskiej, no. 1652, Ser. Math. 91 (2004), 343-355.
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