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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1095,
author = {Adam Woryna},
title = {Representations of a free group of rank two by time-varying Mealy automata},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {25},
year = {2005},
pages = {119-134},
zbl = {1105.20304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1095}
}
Adam Woryna. Representations of a free group of rank two by time-varying Mealy automata. Discussiones Mathematicae - General Algebra and Applications, Tome 25 (2005) pp. 119-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1095/
[000] [1] S.V. Aleshin, A free group of finite automata, (Russian), Vestnik Moskov. Univ. Ser. I. Mat. Mekh. 38 (1983), 12-14 (English Transl.: Moscow Univ. Math. Bull. 38 (1983), No. 4, 10-13). | Zbl 0513.68044
[001] [2] L. Bartholdi, R.I. Grigorchuk and V. Nekrashevych, From fractal groups to fractal sets, 'Fractals in Graz 2001', Birkhäuser, Basel 2003, 25-118. | Zbl 1037.20040
[002] [3] R.I. Grigorchuk, V. V. Nekrashevich and V.I. Sushchanskii, Automata, Dynamical Systems and Groups, Proc. Steklov Inst. Math. 231 (2000), 128-203. | Zbl 1155.37311
[003] [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).
[004] [5] A. Olijnyk, Free products of C2 as groups of finitely automatic permutations, (in Russian), Voprosy Algebry 14 (1999), 158-165.
[005] [6] A.S. Olijnyk and V.I. Sushchanskii, Free Groups of Infinitely Unitriangular Matrices, Math. Notes 67 (2000), 320-324.
[006] [7] V.I. Sushchanskii, Group of Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1998, no. 6, 47-51.
[007] [8] V.I. Sushchanskii, Group of Finite Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1999, no. 2, 48-52.
[008] [9] A. Woryna, On transformations given by time-varying Mealy automata, (Polish), Zeszyty Nauk. Politech. Śląskiej, no. 1581, Ser. Automatyka 138 (2003), 201-215.
[009] [10] A. Woryna, On the group permutations generated by time-varying Mealy automata, Publ. Math. Debrecen, 67 (2005), 115-130. | Zbl 1081.20042
[010] [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.