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The automaton permutation group $AS_n$ generated by elements of infinite order

V. V. Makarov


Abstract: For an arbitrary integer $n\ge2$ we consider the group $AS_n$, constituted by boundedly determinate functions of one variable defined by means of initial automata with finite number of states on the Moore diagram, with input and output alphabets $E_n=\{0,1,\dots,n-1\}$, which at each state $q$ realize the output function $\psi(q,x)$ equal to some permutation $f_q(x)$ on the set $E_n$; $f_q(x)$ is an element of the complete symmetric group $S_n$. For $AS_n$ we give explicit generating system of elements of infinite order.

UDC: 519.713.2

Received: 02.06.1993
Revised: 05.01.1995

DOI: 10.4213/dm486

 English version: Discrete Mathematics and Applications, 1997, 7:5, 455–463

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