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Random Numbers Generation and Testing
200530.1 Definition of a random sequence 715 30.2 Random number generators 717 History • Properties of random number generators • Types of random number generators • Popular random number generators 30.3 Testing of random number generators 722 30.4 Testing a device 722 30.5 Statistical (empirical) tests 723 30.6 Some examples of statistical models on Σ 725
Lange, T., Lubicz, D., Weigl, A.
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Uniform random number generation
Annals of Operations Research, 1994This article provides a survey of pseudorandom number generators (i.e., deterministic recursive formulas from \(\{1, 2,\dots,m\}\) to \(\{1, 2,\dots,m\}\) for a given large prime number \(m\)) that attempt to produce a sequence (here, \(k/m\)) which approximates a sequence of truly independent random variables uniformly distributed over the interval \([
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Occupancy Numbers in Testing Random Number Generators
SIAM Journal on Applied Mathematics, 2002Summary: The classical occupancy problem where \(n\) balls are placed in \(N\) cells is used for testing of random number generators. We show that the statistics of appropriately chosen occupancy numbers are incompatible with the statistics of many pseudorandom number generators (PRNGs) even if they are truncated.
Alexander Figotin +4 more
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Local Randomness in Polynomial Random Number and Random Function Generators
SIAM Journal on Computing, 1993Summary: A distribution on \(n\)-bit strings is called \((\varepsilon,e)\)-locally random, if for every choice of \(e \leq n\) positions the induced distribution on \(e\)-bit strings is in the \(L_ 1\)-norm at most \(\varepsilon\) away from the uniform distribution on \(e\)-bit strings. Local randomness in polynomial random number generators (RNG) that
Harald Niederreiter, Claus-Peter Schnorr
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Random number generation and creativity
Medical Hypotheses, 2008A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers ...
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Seeds for random number generators
Communications of the ACM, 2003Techniques for choosing seeds for social and scientific applications of random number generators.
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Generating Random Factored Numbers, Easily
Journal of Cryptology, 2003In [SIAM J. Comput. 17, No. 2, 179--193 (1988; Zbl 0642.10003)], \textit{E. Bach} presented an efficient algorithm for the generation of uniformly random numbers along with its prime factorization. In this short note, the author presents a significantly simpler algorithm and analysis for this problem.
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Random Number Generation with ⊕-NFAs
2002We prove that unary symmetric difference nondeterministic finite automata have the same state cycle as linear feedback shift registers. This leads to the application of these automata for random number generation.
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On the CRAY-System Random Number Generator
SIMULATION, 1999We present a theoretical and empirical analysis of the quality of the CRAY-system random num ber generator RANF in parallel settings. Sub sequences of this generator are used to obtain parallel streams of random numbers for each pro cessor.
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