On Computing the Total Variation Distance of Hidden Markov Models

04/17/2018

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by   Stefan Kiefer, et al.

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We prove results on the decidability and complexity of computing the total variation distance (equivalently, the L_1-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between the distributions on words that two hidden Markov models induce. The main results are: (1) it is undecidable whether the distance is greater than a given threshold; (2) approximation is #P-hard and in PSPACE.