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The main problem of the paper is related to the algebraic method for determining transition probabilities in probabilistic algorithms interpreted in finite structures. The correctness of this method is based on a lemma stating that the determinant of a matrix (being of a special form) is different from zero. The paper contains two proofs of this lemma, formulated without a proof in [3].
In the paper it is presented an algorithm for generating pseudo-random binary sequences. There are formulated theorems concerning properties of the sequence generated by the algorithm. The sequence is not periodic. Moreover, for any natural number n>0, the initial fragment of the generated sequence of the length (2xn)x2 (2-n) contains all (binary) series of the length n.
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