Long Range Correlations in Linear Congruential Generators
Long Range Correlations in Linear Congruential Generators
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In our eReader you can find the full English version of the book. Read Long Range Correlations in Linear Congruential Generators Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Long Range Correlations in Linear Congruential Generators
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. . , x^_ ^ ) is a permutation of {0, 1, 2, m-1) . For a fixed k, we now ask whether there exists a guaranteed linear relation among entries in the chain separated by 2 ; S c. X - (mod 2^) . (3) J n+j2'^ Substituting (2) into (3), this will be the case for given x^ and b if f(a)xQ - (mod 2^) .
^^^^^ b - (mod 2^ . (4) b k where f(0) - E c. A-^ J The case b - 0, Xq odd, was studied by Filk, Marcu, and Fredenhagen, here one only requires f(a) « (mod 1^-), (5) independently of x„ . The basic relati...on of type (5) is the Euler totient formula' which becomes in the present case a -1=0 (mod 2^) . (6) However, there are numerous polynomials of lower degree that satisfy (5). For relations between {x ) separated by 2, these are most readily generated from the primitive case &- - 1 - (mod 2"^^^^) (7) [31 for suitable 7(k) . The totient formula guarantees that 7(k) > k+1, but the decomposition «k k-1 „j a - 1 - (a-1) n (a + 1) (8) j-0 establishes at once the result that if a ■ 1 (mod 2 ), then 7(k) > k+a.
What to read after Long Range Correlations in Linear Congruential Generators?
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To quickly assess the difficulty of the text, read a short excerpt:
. . , x^_ ^ ) is a permutation of {0, 1, 2, m-1) . For a fixed k, we now ask whether there exists a guaranteed linear relation among entries in the chain separated by 2 ; S c. X - (mod 2^) . (3) J n+j2'^ Substituting (2) into (3), this will be the case for given x^ and b if f(a)xQ - (mod 2^) .
^^^^^ b - (mod 2^ . (4) b k where f(0) - E c. A-^ J The case b - 0, Xq odd, was studied by Filk, Marcu, and Fredenhagen, here one only requires f(a) « (mod 1^-), (5) independently of x„ . The basic relati...on of type (5) is the Euler totient formula' which becomes in the present case a -1=0 (mod 2^) . (6) However, there are numerous polynomials of lower degree that satisfy (5). For relations between {x ) separated by 2, these are most readily generated from the primitive case &- - 1 - (mod 2"^^^^) (7) [31 for suitable 7(k) . The totient formula guarantees that 7(k) > k+1, but the decomposition «k k-1 „j a - 1 - (a-1) n (a + 1) (8) j-0 establishes at once the result that if a ■ 1 (mod 2 ), then 7(k) > k+a.
What to read after Long Range Correlations in Linear Congruential Generators?
You can find similar books in the "Read Also" column, or choose other free books by O E Percus to read onlineMoreLess
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