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We provide a rigorous definition of a certain kind of characterization forcapacity regions of a family of Markoff networks which is based on optimizationproblems resulting out of calculating conditional mutual information from afinite number of random variables and by constraining these random variables ina certain way. This definition is partly motivated by the definition ofsingle-letter characterizations in information theory. For a point-to-pointMarkoff channel, we prove that approximating the solution to thesecharacterizations within an additive constant is a computable problem. Based onprevious undecidability results concerning capacities of certain class offinite state machine channels (FSMCs), it will follow that there exists anexample of family of FSMCs for which given such a characterization, thischaracterization cannot represent the capacity of this family of FSMCs.

Non-existence of certain kind of finite-letter mutual information characterization for a class of time-invariant Markoff channels