When does feedback not increase capacity for channels with memory?

In this work, we investigate the channels with memory for which feedback does not help to increase their capacity. For this purpose, we consider finite-state Markov (FSM) channels and we first present a symmetric classification for these channels which is similar to the symmetry classification for discrete memoryless channels. We show that for these type of channels feedback capacity is achieved by uniform independent and identically distributed input policies and we show this using the dynamic programming technique.