Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
We study Markov chains via invariants constructed from periodic orbits. Canonical extensions, based on these invariants, are used to establish a constraint on the degree of finite-to-one block homomorphisms from one Markov chain to another. We construct a polytope from the normalized weights of periodic orbits. Using this polytope, we find canonically-defined induced Markov chains inside the original Markov chain. Each of the invariants associated with these Markov chains gives rise to a scaffold of invariants for the original Markov chain. This is used to obtain counterexamples to the finite equivalence conjecture and to a conjecture regarding finitary isomorphism with finite expected coding time. Also included are results related to the problem of minimality (with respect to block homomorphism) of Bernoulli shifts in the class of Markov chains with beta function equal to the beta function of the Bernoulli shift. © 1991, Cambridge University Press. All rights reserved.
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
Heng Cao, Haifeng Xi, et al.
WSC 2003
Jianke Yang, Robin Walters, et al.
ICML 2023
M.B. Small, R.M. Potemski
Proceedings of SPIE 1989