Exact Synchronization for Finite-State Sources

TL;DR

This paper investigates the conditions and rates at which an observer can exactly synchronize to a finite-state source using epsilon-machines, providing analytical tools and algorithms for testing and understanding synchronization speed.

Contribution

It introduces a method to analytically compute the synchronization rate for exact epsilon-machines and offers an efficient algorithm to test for exactness.

Findings

Observers synchronize exponentially fast on average.

Prediction accuracy approaches optimal exponentially fast.

Provided polynomial-time algorithm for testing epsilon-machine exactness.

Abstract

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.