Geodesic
On the completeness of systems of finite automata
Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 74-78.

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For an arbitrary alphabet $A$, we construct a recursive set of bases of automata with a single output and no more than two inputs, with algorithmically unsolvable completeness problem. The result is final, because the bases of automata with a single input and single output are incomplete. 
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     author = {V. A. Orlov},
     title = {On the completeness of systems of finite automata},
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V. A. Orlov. On the completeness of systems of finite automata. Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 74-78. http://geodesic.mathdoc.fr/item/DM_1997_9_2_a6/