Geodesic
On the algorithmic undecidability of $A$-completeness for the boundedly determinate functions
Matematičeskie zametki, Tome 11 (1972) no. 6, pp. 687-697.

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A functional system $P$ is considered, whose elements are functions realized by the so-called finite automata and known as the boundedly determinate functions (B. D. functions) and whose operations are known as the operations of superposition. The system $\mathfrak{M}$ of B.D. functions is called $A$-complete if, for an arbitrary B. D. function and for every natural number $\tau>0$, we can obtain (with the help of the operations of superposition) a B. D. function coinciding with the given one of all the words of lenth $\tau$ from the B. D. functions of the system $\mathfrak{M}$. The question is: does there exist an algorithm for deciding the $A$-completeness of an arbitrary finite system of B. D. functions? It is shown that such an algorithm does not exist (see [4]). 
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     author = {V. A. Buevich},
     title = {On the algorithmic undecidability of $A$-completeness for the boundedly determinate functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {687--697},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_6_a9/}
}
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V. A. Buevich. On the algorithmic undecidability of $A$-completeness for the boundedly determinate functions. Matematičeskie zametki, Tome 11 (1972) no. 6, pp. 687-697. http://geodesic.mathdoc.fr/item/MZM_1972_11_6_a9/