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. Previous examples of
infinite excess entropy processes over finite alphabets admit only invariant
HMM presentations with uncountable state sets.Comment: 13 pages, 3 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/ieepcsg.ht