ABOUT TESTING THE DENSE EMBEDDING HYPOTHESIS FOR DISCRETE RANDOM SEQUENCES // BSU bulletin. Mathematics, Informatics. - 2017. №4. . - С. 9-20.

ABOUT TESTING THE DENSE EMBEDDING HYPOTHESIS FOR DISCRETE RANDOM SEQUENCES

The dense embedding hypothesis says that one discrete sequence can be embedded in the other in such a way that the characters of the inserted se- quence are separated in the resulting sequence by at most one character. We propose a sequential test for the dense imbedding hypothesis for discrete equiprobable random sequences over a finite alphabet and study its properties. The probability of type I error (the probability of rejection of the dense embed- ding hypothesis when it’s true) of the constructed test equals zero. We derive an expression for the probability of type II error under the alternative hypothe- sis that the discrete sequences under consideration are independent. A class of similar test is also considered. It turns out that a small change in the testing procedure greatly changes the error probabilities. A numerical illustration and discussion of the results are given.

dense embedding; sequential test; hypothesis of independence; probabilities of type I and type II errors; discrete random sequence.