Geodesic
Estimation for an output symbol multiplicity in invertible automata
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014).

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the maximum repetition number for an output symbol in the output table of an invertible automaton with $n$ states and $m$ input symbols is $[(n+1)/2][(n+2)/2]$ if $[(n+2)/2]\leq m$, or $(n-m+1)m$ otherwise.
Keywords: finite automata, invertibility, weakly invertibility, strongly invertibility, output symbol multiplicity. 
@article{PDMA_2014_7_a59,
     author = {D. A. Katerinskiy},
     title = {Estimation for an output symbol multiplicity in invertible automata},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {141},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a59/}
}
TY  - JOUR
AU  - D. A. Katerinskiy
TI  - Estimation for an output symbol multiplicity in invertible automata
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2014
SP  - 141
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2014_7_a59/
LA  - ru
ID  - PDMA_2014_7_a59
ER  - 
%0 Journal Article
%A D. A. Katerinskiy
%T Estimation for an output symbol multiplicity in invertible automata
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2014
%P 141
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2014_7_a59/
%G ru
%F PDMA_2014_7_a59
D. A. Katerinskiy. Estimation for an output symbol multiplicity in invertible automata. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014). http://geodesic.mathdoc.fr/item/PDMA_2014_7_a59/

[1] Kurmit A. A., Avtomaty bez poteri informatsii konechnogo poryadka, Zinatne, Riga, 1972

[2] Tao R. J., Finite automata and application to cryptography, Springer, Tsinghua, 2008 | MR