Minimal auxiliary Markov chains through sequential elimination of states

When using an auxiliary Markov chain to compute the distribution of a pattern statistic, the computational complexity is directly related to the number of Markov chain states. Theory related to minimal deterministic finite automata have been applied to large state spaces to reduce the number of Mark...

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Bibliographic Details
Published inCommunications in statistics. Simulation and computation Vol. 48; no. 4; pp. 1040 - 1054
Main Author Martin, Donald E. K.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 21.04.2019
Subjects
completion strings
failure states
Markov chain embedding
minimal deterministic finite automaton
spaced seed coverage
structured motifs
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Summary:When using an auxiliary Markov chain to compute the distribution of a pattern statistic, the computational complexity is directly related to the number of Markov chain states. Theory related to minimal deterministic finite automata have been applied to large state spaces to reduce the number of Markov chain states so that only a minimal set remains. In this paper, a characterization of equivalent states is given so that extraneous states are deleted during the process of forming the state space, improving computational efficiency. The theory extends the applicability of Markov chain based methods for computing the distribution of pattern statistics.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2017.1406505