Geodesic
On completeness and $A$-completeness of $S$-sets of determinate functions containing all one-place determinate $S$-functions
Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 75-87.

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We consider the problem on completeness of sets of $S$-functions, the determinate functions such that the automaton calculating them realises in each state functions which emanate no value. We assume that each set of $S$-functions whose completeness is checked in this paper contains all $S$-functions depending on at most one variable. We describe all $A$-precomplete classes of such sets. It is shown that there exists an algorithm recognising $A$-completeness of $S$-sets of one-place determinate functions containing all one-place determinate $S$-functions. 
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M. A. Podkolzina. On completeness and $A$-completeness of $S$-sets of determinate functions containing all one-place determinate $S$-functions. Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 75-87. http://geodesic.mathdoc.fr/item/DM_2009_21_2_a3/

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