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Exact Synchronization for Finite-State Sources

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Abstract

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the ϵ-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 ϵ-machines and provide an efficient polynomial-time algorithm to test ϵ-machines for exactness.

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Authors and Affiliations

  1. Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    Nicholas F. Travers & James P. Crutchfield

  2. Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    Nicholas F. Travers & James P. Crutchfield

  3. Physics Department, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    James P. Crutchfield

  4. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

    James P. Crutchfield

Authors
  1. Nicholas F. Travers
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  2. James P. Crutchfield
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Correspondence to James P. Crutchfield.

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Travers, N.F., Crutchfield, J.P. Exact Synchronization for Finite-State Sources. J Stat Phys 145, 1181–1201 (2011). https://doi.org/10.1007/s10955-011-0342-4

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  • DOI: https://doi.org/10.1007/s10955-011-0342-4

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