Abstract:
In this paper we study the existence and uniqueness of a concave continuation to the segment $[0,k-1]$ of an arbitrary unary function of $k$-valued logic $f_{L}:\{0,1,\ldots,k-1\}\to\{0,1,\ldots,k-1\}$ for any natural $k \geq 2$. As a result of the study, for an arbitrary natural $k \geq 2$ we formulate and prove a criterion for the existence of a concave continuation of a unary function of $k$-valued logic $f_{L}$. It is proved that the found criterion for the existence of a concave continuation of a function of $k$-valued logic $f_{L}$ is also a criterion for the existence of a minimal concave continuation of a function of $k$-valued logic $f_{L}$, but is not a sufficient condition for the uniqueness of a concave continuation of a function of $k$-valued logic $f_{L}$. We also find and prove a criterion for the uniqueness of a concave continuation of an arbitrary unary function of $k$-valued logic $f_{L}$.
Keywords:function of $k$-valued logic, concave continuation of a function of $k$-valued logic, criterion for the existence and uniqueness of a concave continuation.
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