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The paper addresses the problem of computing reducts in decision tables where attributes are assigned costs. Computing reducts has been an interesting issue as the reducts may be successfully applied in further analyses of the decision table. In systems where attribute are assigned costs, the problem of reduct generation may be reformulated to that of finding reducts satisfying some additional constraints, in particular reducts of minimal attribute costs. The constraints allow to incorporate external preference into the system and, additionally, simplify the problem of interpreting the obtained results, since the number of reducts of minimal costs, as opposed to the number of all existing reducts, is usually very small. This paper introduces a new algorithm for generating all reducts of minimal costs, called minimal cost reducts or cheapest reducts. The practical behaviour of this algorithm has been tested in …