Related papers: Period of the d-Sequence Based Random Number Gener…
Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
We develop a new approach for uniform generation of combinatorial objects, and apply it to derive a uniform sampler REG for d-regular graphs. REG can be implemented such that each graph is generated in expected time O(nd^3), provided that…
The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length…
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…
A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device,…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
This paper presents a comparison of the quality of randomness of D sequences based on diehard tests. Since D sequences can model any random sequence, this comparison is of value beyond this specific class.
We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
In this paper, a new pseudo-random number generator (PRNG) based on chaotic iterations is proposed. This method also combines the digits of two XORshifts PRNGs. The statistical properties of this new generator are improved: the generated…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…
Quantum random number generators (QRNGs) produce random numbers based on the intrinsic probabilistic nature of quantum mechanics, making them true random number generators (TRNGs). In this paper, we design and fabricate an embedded QRNG…
The paper examines the structure of the periodic continued fraction for $\sqrt{d}$ and gives formulae for the central term as well as the repeated partial quotients occurring in its period.
In this article, we propose a new counter-based implementation of John von Neumann's middle-square random number generator (RNG). Several rounds of squaring are applied to a counter to produce a random output. We discovered that four rounds…
In this paper we present experiments in order to show how some pseudo random number generators can improve the effectiveness of a statistical cryptanalysis algorithm. We deduce mainly that a better generator enhance the accuracy of the…
The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions…