1,849 research outputs found

    A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

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    In today's world, several applications demand numbers which appear random but are generated by a background algorithm; that is, pseudo-random numbers. Since late 19th19^{th} century, researchers have been working on pseudo-random number generators (PRNGs). Several PRNGs continue to develop, each one demanding to be better than the previous ones. In this scenario, this paper targets to verify the claim of so-called good generators and rank the existing generators based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far has been explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, well-known generators have been chosen for empirical testing. Two types of empirical testing has been done on each PRNG -- blind statistical tests with Diehard battery of tests, TestU01 library and NIST statistical test-suite and graphical tests (lattice test and space-time diagram test). Finally, the selected 2929 PRNGs are divided into 2424 groups and are ranked according to their overall performance in all empirical tests

    Controlled non uniform random generation of decomposable structures

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    Consider a class of decomposable combinatorial structures, using different types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the random generation of such structures with respect to a size nn and a targeted distribution in kk of its \emph{distinguished} atoms. We consider two variations on this problem. In the first alternative, the targeted distribution is given by kk real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 < \TargFreq_i < 1 for all ii and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We aim to generate random structures among the whole set of structures of a given size nn, in such a way that the {\em expected} frequency of any distinguished atom \At_i equals \TargFreq_i. We address this problem by weighting the atoms with a kk-tuple \Weights of real-valued weights, inducing a weighted distribution over the set of structures of size nn. We first adapt the classical recursive random generation scheme into an algorithm taking \bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw mm structures from the \Weights-weighted distribution. Secondly, we address the analytical computation of weights such that the targeted frequencies are achieved asymptotically, i. e. for large values of nn. We derive systems of functional equations whose resolution gives an explicit relationship between \Weights and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in \bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies associated with a given kk-tuple \Weights of weights, and an optimized version in \bigO{k n^2} in the case of context-free languages. This allows for a heuristic resolution of the weights/frequencies relationship suitable for complex specifications. In the second alternative, the targeted distribution is given by a kk natural numbers n1,…,nkn_1, \ldots, n_k such that n1+⋯+nk+r=nn_1+\cdots+n_k+r=n where r≥0r \geq 0 is the number of undistinguished atoms. The structures must be generated uniformly among the set of structures of size nn that contain {\em exactly} nin_i atoms \At_i (1≤i≤k1 \leq i \leq k). We give a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating mm structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for regular specifications

    The LUT-SR Family of Uniform Random Number Generators for FPGA Architectures

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