Related papers: Dichotomic random number generators
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
We construct a pseudorandom generator which fools read-$k$ oblivious branching programs and, more generally, any linear length oblivious branching program, assuming that the sequence according to which the bits are read is known in advance.…
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…
We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…
In this paper, we develop a new cellular automata-based linear model for several nonlinear pseudorandom number generators with practical applications in symmetric cryptography. Such a model generates all the solutions of linear binary…
random_tree() is a linear time and space C++ implementation able to create trees of up to a billion nodes for genetic programming and genetic improvement experiments. A 3.60GHz CPU can generate more than 18 million random nodes for GP…
We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic…
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy.…
Let T d (n) be the set of d-ary rooted trees with n internal nodes. We give a method to construct a sequence (t n , n $\ge$ 0) where, for any n $\ge$ 1, t n has the uniform distribution in T d (n), and t n is constructed from t n--1 by the…
We propose a method for program generation based on semantic scaffolds, lightweight structures representing the high-level semantic and syntactic composition of a program. By first searching over plausible scaffolds then using these as…
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…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
Let $1<g_1<\ldots<g_{\varphi(p-1)}<p-1$ be the ordered primitive roots modulo~$p$. We study the pseudorandomness of the binary sequence $(s_n)$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod 2$, $n=0,1,\ldots$. In particular, we study the…
It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels…
Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…
Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to…
Pseudo-Random Numbers Generators (PRNGs) are algorithms produced to generate long sequences of statistically uncorrelated numbers, i.e. Pseudo-Random Numbers (PRNs). These numbers are widely employed in mid-level cryptography and in…