Geodesic
The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities\footnote{The paper is published by the recommendation of the Program Commitee of the CTCrypt'2016 Conference.}
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 24-37

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We consider the classical model of embeddings in a simple binary Markov chain with unknown transition probability matrix. We obtain conditions on the asymptotic growth of lengths of the original and embedded sequences sufficient for the consistency of the proposed statistical embedding detection test.
Keywords: Markov chain, embeddings, statistical test. 
@article{DM_2017_29_3_a1,
     author = {A. V. Volgin},
     title = {The square root law in the embedding detection problem for {Markov} chains with unknown matrix of transition {probabilities\footnote{The} paper is published by the recommendation of the {Program} {Commitee} of the {CTCrypt'2016} {Conference.}}},
     journal = {Diskretnaya Matematika},
     pages = {24--37},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_3_a1/}
}
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A. V. Volgin. The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities\footnote{The paper is published by the recommendation of the Program Commitee of the CTCrypt'2016 Conference.}. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 24-37. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a1/