  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
$n$.
