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Bibliographic description:
Mezhennaya N. М.
АВОUТ А TEST OF EMBEDDING WIТH МARGIN FOR DISCRETE SEQUENCES // BSU bulletin. Mathematics, Informatics. - 2018. №4. . - С. 3-15.
Title:
АВОUТ А TEST OF EMBEDDING WIТH МARGIN FOR DISCRETE SEQUENCES
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-4-3-15UDK: 519.244.2, 519.244.8
Annotation:
Sequence Х is а subsequence with margin d о[ sequence У if Х is constructed from У Ьу deleting non-adjacent segments consisted of at most d letters. 1n this case we saу that Х can Ье embedded into У with margin d. Тhе article presents а sequential test for the hypothesis of embedding with margin d for discrete random sequences over а finite alphabet and study its properties. Тhе probaЬility of type I error (the probaЬility of re­ jection of true hypothesis of embedding with margin) of the constructed test is equal to zero. We derive an expression for the probaЬility of type II error under the altemative hypothesis that the discrete sequences under consideration consist of mutually inde­ pendent random variaЫes with uniform distributions on finite alphaЬet. Wе find out the average number of letters of the embedded sequence used Ьу test before the decision is made under the altemative hypothesis. Тhе complexity of the proposed procedure is proportional to the length of the embedded sequence under true hypothesis of embed­ ding with margin and is smaller under the altemative hypothesis which is less than complexity oftotal testing Ьу order ofmagnitude. We have presented numerical values of the probaЬility of type II error and the average number of used letters for different values of d and the alphabet size.
Keywords:
dense embedding; embedding with margin; sequential test; hypothesis of independence; probaЬilities of type I and type II errors; discrete random sequence.
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