In this paper, classes of decision tables closed with respect to deletion of attributes (columns) and change of decisions are considered. For tables from these classes, the dependence of the minimum complexity of regular decision trees on the minimum complexity of oblivious decision trees, in which the order of queries on attribute values is predetermined, is studied. It is proved that the function describing this dependence is either bounded from above by a constant or grows as a logarithm, or grows almost linearly. This result is valid for the so-called bounded complexity measures, including the depth and weighted depth of decision trees. It is also shown that the minimum complexity of an oblivious tree for a decision table is equal to the minimum complexity of a reduct for this table.

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Comparison of Complexity of Regular and Oblivious Decision Trees for Decision Tables from Closed Classes

  • Azimkhon Ostonov,
  • Mikhail Moshkov

摘要

In this paper, classes of decision tables closed with respect to deletion of attributes (columns) and change of decisions are considered. For tables from these classes, the dependence of the minimum complexity of regular decision trees on the minimum complexity of oblivious decision trees, in which the order of queries on attribute values is predetermined, is studied. It is proved that the function describing this dependence is either bounded from above by a constant or grows as a logarithm, or grows almost linearly. This result is valid for the so-called bounded complexity measures, including the depth and weighted depth of decision trees. It is also shown that the minimum complexity of an oblivious tree for a decision table is equal to the minimum complexity of a reduct for this table.