Extended BRS algebra and color confinement criteria

We examine the color-confinement criteria which were proposed by Kugo and Ojima on the basis of the Becchi-Rouet-Stora (BRS) symmetry. With the use of Nakanishi's theorem and the ghost conjugation, we look for the representations of the extended BRS algebra compatible with one of their criteria (the K-O condition) and then ask whether or not they are physically acceptable. As a result, the basic BRS cancellation mechanism does not work, and the K-O condition is not regarded as a confinement condition.