In this paper, we consider classes of decision tables with many-valued decisions closed relative to removal of attributes (columns) and changing sets of decisions assigned to rows. For tables from an arbitrary closed class, we study a function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ that characterizes the dependence in the worst case of the minimum complexity of deterministic decision trees on the minimum complexity of nondeterministic decision trees. Note that nondeterministic decision trees for a decision table can be interpreted as a way to represent an arbitrary system of true decision rules for this table that cover all rows. We indicate the condition for the function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ to be defined everywhere. If this function is everywhere defined, then it is either bounded from above by a constant or is greater than or equal to $n$ for infinitely many $n$. In particular, for any nondecreasing function $\varphi$ such that $\varphi (n)\geq n$ and $\varphi (0)=0$, the function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ can grow between $\varphi (n)$ and $\varphi (n)+n$. We indicate also conditions for the function $\mathcal{H}^{\infty}_{\psi,A}(n)$ to be bounded from above by a polynomial on $n$.

翻译：本文考虑封闭类中多值决策表，此类表在移除属性（列）和更改行分配决策集的操作下保持封闭性。对于任意封闭类中的表，我们研究函数$\mathcal{H}^{\infty}_{\psi ,A}(n)$，该函数刻画了在最坏情况下确定性决策树的最小复杂度与非确定性决策树的最小复杂度之间的依赖关系。值得注意的是，决策表的非确定性决策树可视为表示该表所有覆盖行的任意真决策规则系统的方式。我们给出了函数$\mathcal{H}^{\infty}_{\psi ,A}(n)$全局定义的条件。若该函数全局定义，则要么有常数上界，要么在无穷多个$n$上满足$\mathcal{H}^{\infty}_{\psi ,A}(n)\geq n$。特别地，对任意满足$\varphi (n)\geq n$且$\varphi (0)=0$的非递减函数$\varphi$，函数$\mathcal{H}^{\infty}_{\psi ,A}(n)$的增长速率可介于$\varphi (n)$与$\varphi (n)+n$之间。此外，我们给出了$\mathcal{H}^{\infty}_{\psi,A}(n)$具有多项式上界的条件。