1,849 research outputs found
A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies
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 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 PRNGs are divided into groups and are
ranked according to their overall performance in all empirical tests
Controlled non uniform random generation of decomposable structures
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 and a targeted
distribution in of its \emph{distinguished} atoms. We consider two
variations on this problem. In the first alternative, the targeted distribution
is given by real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 <
\TargFreq_i < 1 for all and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We
aim to generate random structures among the whole set of structures of a given
size , 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 -tuple \Weights of real-valued weights, inducing a weighted
distribution over the set of structures of size . 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 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 . 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 -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 natural numbers such that
where is the number of undistinguished atoms.
The structures must be generated uniformly among the set of structures of size
that contain {\em exactly} atoms \At_i (). We give
a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating
structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for
regular specifications
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