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Nicholas F. Travers and
James P. Crutchfield |
ABSTRACT: We present two examples of finite-alphabet, infinite excess entropy processes generated by invariant hidden Markov models (HMMs) with countable state sets. The first, simpler example is not ergodic, but the second is. It appears these are the first constructions of processes of this type in the literature. Previous examples of infinite excess entropy processes over finite alphabets admit only invariant HMM presentations with uncountable state sets.