# On a group-matrix type automaton with output

TL;DR: A new type of representation of a strongly connetted group-matrix type automaton of order n on G with output or an (n, O)automaton with output is introduced.

Abstract: In this paper some results of [6] are extended for a strongly connected groupmatrix type automaton with output. A new type of representation of a strongly connetted group-matrix type automaton of order n on G with output or an (n, O)automaton with output is introduced. Using this representation we prove some important results on automorphism groups of a strongly connected (n, G)-automaton with output and also on a strongly connected abelian (n, G)-automaton with output.

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131 citations

### "On a group-matrix type automaton wi..." refers background in this paper

...This means that A' is regular. (Cf. Lemma 3.1 in [ 5 ].)...

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...[ 5 ]]. Now Theorem 3.2 implies that e($)= =~TJ(x)=$=0(~)....

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...[ 5 ]]. This implies that Z(s, a)=Z'(Q(s), a) where Z' is the output-function of the (n, G(A))automaton....

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### "On a group-matrix type automaton wi..." refers background in this paper

...Lemma 1 and Theorem 2 proved in [ 4 ] can be easily extended as follows:...

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### "On a group-matrix type automaton wi..." refers background or methods in this paper

...4 in [6]....

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...In this paper some results of [6] are extended for a strongly connected groupmatrix type automaton with output....

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...The above theorem was proved in [6] only for a (1, G)-automaton without output....

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...Now in order to construct a group-matrix type automaton of order n on G or an (n, G)-automaton we recall some important definitions introduced in [6]....

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