Introduction to algorithms
Elements of information theory
Elements of information theory
On the Computational Complexity of Approximating Distributions by Probabilistic Automata
Machine Learning - Computational learning theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Metrics and Similarity Measures for Hidden Markov Models
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
Two Methods for Improving Performance of a HMM and their Application for Gene Finding
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
A Hidden Markov Model for Predicting Transmembrane Helices in Protein Sequences
ISMB '98 Proceedings of the 6th International Conference on Intelligent Systems for Molecular Biology
Some computational complexity results for synchronous context-free grammars
HLT '05 Proceedings of the conference on Human Language Technology and Empirical Methods in Natural Language Processing
The most probable annotation problem in HMMs and its application to bioinformatics
Journal of Computer and System Sciences
Computation of distances for regular and context-free probabilistic languages
Theoretical Computer Science
Absolute Convergence of Rational Series Is Semi-decidable
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Viterbi training for PCFGs: hardness results and competitiveness of uniform initialization
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
A lower bound for learning distributions generated by probabilistic automata
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Absolute convergence of rational series is semi-decidable
Information and Computation
On the computation of some standard distances between probabilistic automata
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
Finding the most probable string and the consensus string: an algorithmic study
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
Bayesian network automata for modelling unbounded structures
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
On the complexity of computing probabilistic bisimilarity
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing the probability of generating a given string, or computing the most likely path generating a given string. In this paper we consider the problem of computing the most likely string, or consensus string, generated by a given model, and its implications on the complexity of comparing hidden Markov models. We show that computing the consensus string, and approximating its probability within any constant factor, is NP-hard, and that the same holds for the closely related labeling problem for class hidden Markov models. Furthermore, we establish the NP-hardness of comparing two hidden Markov models under the L∞- and L1-norms. We discuss the applicability of the technique used for proving the hardness of comparing two hidden Markov models under the L1-norm to other measures of distance between probability distributions. In particular, we show that it cannot be used for proving NP-hardness of determining the Kullback-Leibler distance between two hidden Markov models, or of comparing them under the Lk-norm for any fixed even integer k.