Comparison of Deterministic and Nondeterministic Decision Trees for Decision Tables with Many-valued Decisions from Closed Classes

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 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 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 for infinitely many . In particular, for any nondecreasing function such that and , the function can grow between and . We indicate also conditions for the function to be bounded from above by a polynomial on .

Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST).



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