Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-08-25
Nonlinear Sciences
Chaotic Dynamics
9 pages, 6 figures; now includes analytical calculation of the synchronization rate; updates and corrections added
Scientific paper
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.
Crutchfield James P.
Travers Nicholas F.
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