  We analyze how an observer synchronizes to the internal state of a
finite-state information source, using the epsilon-machine causal
representation. Here, we treat the case of exact synchronization, when it is
possible for the observer to synchronize completely after a finite number of
observations. The more difficult case of strictly asymptotic synchronization is
treated in a sequel. In both cases, we find that an observer, on average, will
synchronize to the source state exponentially fast and that, as a result, the
average accuracy in an observer's predictions of the source output approaches
its optimal level exponentially fast as well. Additionally, we show here how to
analytically calculate the synchronization rate for exact epsilon-machines and
provide an efficient polynomial-time algorithm to test epsilon-machines for
exactness.
