On Finding All Reducts of Consistent Decision Tables

The problem of finding reducts plays an important role in processing information on decision tables. The objective of the attribute reduction problem is to reject a redundant attribute in order to find a core attribute for data processing. The attribute reduction in decision tables is the process of finding a minimal subset of conditional attributes which preserve the classification ability of decision tables. In this paper we present the time complexity of the problem of finding all reducts of a consistent decision table. We prove that this time complexity is exponential with respect to the number of attributes of the decision tables. Our proof is performed in two steps. The first step is to show that there exists an exponential algorithm which finds all reducts. The other step is to prove that the time complexity of the problem of finding all reducts of a decision table is not less than exponential.