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We comment on some conceptual and and technical problems related tocomputational mechanics, point out some errors in several papers, andstraighten out some wrong priority claims. We present explicitly the correctalgorithm for constructing a minimal unifilar hidden Markov model("$\epsilon$-machine") from a list of forbidden words and (exact) wordprobabilities in a stationary stochastic process, and we comment on inferencewhen these probabilities are only approximately known. In particular we proposeminimization of forecasting complexity as an alternative basis for statisticalinference of time series, in contrast to the traditional maximum entropyprinciple. We present a simple and precise way of estimating excess entropy(aka "effective measure complexity". Most importantly, however, we clarify somebasic conceptual problems. In particular, we show that there exist simplemodels (called "totally recurrent graphs") where none of the nodes of the"$\epsilon$-machine" (the "causal states") corresponds to an element of a state(or history) space partition.

Some comments on computational mechanics, complexity measures, and all that