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The authors thank S.A. Pirogov for finding an error in the proof of the main theorem of our paper “On Error-free Filtering of Finite-State Singular Processes under Dependent Distortions” (Probl. Peredachi Inf., 2007, vol. 43, no. 4, pp. 271–279). The statement of the theorem remains valid (even without additional assumption on finiteness of the number of values of a completely singular process X) if Y is an output process of a stationary memoryless channels whose input signal is X. However, in the general case, where Y is absolutely regular with respect to X, the question of validity of the theorem statement remains open.

Remark on “On Error-free Filtering of Finite-State Singular Processes under Dependent Distortions” published in Probl. Peredachi Inf., 2007, no. 4