Geodesic
Approximate models of permutation automata
Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 103-122
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On the basis of metric properties of output sequences of finite automata approximate models for connected permutational automata, i.e., permutational automata with lesser number of states, are constructed. 
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A. V. Babash. Approximate models of permutation automata. Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 103-122. http://geodesic.mathdoc.fr/item/DM_1997_9_1_a8/