Information accessibility and cryptic processes

We give a systematic expansion of the crypticity-a recently introduced measure of the inaccessibility of a stationary process's internal state information. This leads to a hierarchy of k-cryptic processes and allows us to identify finite-state processes that have infinite cryptic order-the inte...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-09, Vol.42 (36), p.362002-362002 (17)
Main Authors: Mahoney, John R, Ellison, Christopher J, Crutchfield, James P
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:We give a systematic expansion of the crypticity-a recently introduced measure of the inaccessibility of a stationary process's internal state information. This leads to a hierarchy of k-cryptic processes and allows us to identify finite-state processes that have infinite cryptic order-the internal state information is present across arbitrarily long, observed sequences. The crypticity expansion is exact in both the finite- and infinite-order cases. It turns out that k-crypticity is complementary to the Markovian finite-order property that describes state information in processes. One application of these results is an efficient expansion of the excess entropy-the mutual information between a process's infinite past and infinite future-that is finite and exact for finite-order cryptic processes.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/36/362002