  In this paper, we consider the problem of evaluating capacity expression of a
multiple access channel (MAC) with noiseless feedback. So far, the capacity
expression for this channel is known through a multi letter directed
information by Kramer [1]. Recently, it was shown in [2] that one can pose it
as a dynamic optimization problem, however, no dynamic program was provided as
the authors claimed there is no notion of state that is observed by both the
senders. In this paper, we build upon [2] to show that there indeed exists a
state and therefore a dynamic program (DP) that decomposes this dynamic
optimization problem, and equivalently a Bellman fixed-point equation to
evaluate capacity of this channel. We do so by defining a common belief on
private messages and private beliefs of the two senders, and using this common
belief as state of the system. We further show that this DP can be further
reduced to a DP with state as the common belief on just the messages. This
provides a single letter characterization of the capacity of this channel.
