  We consider finite state channels where the state of the channel is its
previous output. We refer to these as POST (Previous Output is the STate)
channels. We first focus on POST($\alpha$) channels. These channels have binary
inputs and outputs, where the state determines if the channel behaves as a $Z$
or an $S$ channel, both with parameter $\alpha$. %with parameter $\alpha.$ We
show that the non feedback capacity of the POST($\alpha$) channel equals its
feedback capacity, despite the memory of the channel. The proof of this
surprising result is based on showing that the induced output distribution,
when maximizing the directed information in the presence of feedback, can also
be achieved by an input distribution that does not utilize of the feedback. We
show that this is a sufficient condition for the feedback capacity to equal the
non feedback capacity for any finite state channel. We show that the result
carries over from the POST($\alpha$) channel to a binary POST channel where the
previous output determines whether the current channel will be binary with
parameters $(a,b)$ or $(b,a)$. Finally, we show that, in general, feedback may
increase the capacity of a POST channel.
