On the Design of LIL Tests for (Pseudo) Random Generators and Some Experimental Results

NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to construct functions that are considered as GOOD pseudorandom generators by NIST SP800-22 test suite though the output of these functions are easily distinguishable from the uniform distribution. Thus these functions are not pseudorandom generators by definition. On the other hand, NIST SP800-22 does not cover some of the important laws for randomness. Two fundamental limit theorems about random binary strings are the central limit theorem and the law of the iterated logarithm (LIL). Several frequency related tests in NIST SP800-22 cover the central limit theorem while no NIST SP800-22 test covers LIL. This paper proposes techniques to address the above challenges that NIST SP800-22 testing suite faces. Firstly, we propose statistical distance based testing techniques for (pseudo) random generators to reduce the above mentioned Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based statistical testing techniques, calculate the probabilities, and carry out experimental tests on widely used pseudorandom generators by generating around 30TB of pseudorandom sequences. The experimental results show that for a sample size of 1000 sequences (2TB), the statistical distance between the generated sequences and the uniform distribution is around 0.07 (with $0$ for statistically indistinguishable and $1$ for completely distinguishable) and the root-mean-square deviation is around 0.005

Analog, hybrid, and digital simulation

Analog, hybrid, and digital computerized simulation technique

Application of advanced on-board processing concepts to future satellite communications systems: Bibliography

Abstracts are presented of a literature survey of reports concerning the application of signal processing concepts. Approximately 300 references are included

Waiting times in a two-queue model with exhaustive and Bernoulli service

Network Analysis;operations research

The effect of pseudo-random number bias on the simulation of a data collection system

The question of the effect of biased pseudo-random numbers on simulation results arises in a majority of industrial simulation applications. Results of the simulations were statistically analyzed

Bandwidth compression of sonar displays

A major problem affecting the design of data compression systems is that of employing a buffer of limited size and at the same time prevent uncontrollable loss of data due to overflow. One method of alleviating this problem is to employ an adaptive compression algorithm. With this design approach when overflow is imminent the compression algorithm is degraded which effectively reduces the input rate to the buffer. A method is proposed here, where by using a recirculating register as the buffer the recirculating data controls the input rate and hence the performance of the system. The system has been analysed for a Poisson input process, and simulated using synthetic patterns similar to that encountered on sonar displays. The results indicate that this form of storage is quantitatively similar to random-access storage but qualitatively superior due to the random nature of the losses. An experimental system has been built using dynamic MOS shift registers for the store and a simple run-length coding procedure

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Event generation on quantum computers

The synthesis of high quality simulated data from event generators is essential in the search for new physics at collider experiments. Modern event generator algorithms use Monte Carlo processes to simulate the evolution of an event from the collision of high energy particles to the formation of long-lived particles. One of the major building blocks of the event generation process is the QCD parton shower. However, despite being a key aspect of modern event generation, the core algorithms which simulate the showering process have remained unchanged since the 1980s, and will become a limiting factor as we move to an era of higher energy and higher luminosity experiments. With the rapid development of quantum computation, dedicated algorithms are required which exploit the potential that quantum computing provides to address problems in high energy physics. In this thesis, we present three novel quantum algorithms for the simulation of a QCD parton shower. The first algorithm provides a proof-of-principle, classical Monte Carlo inspired approach with the ability to simulate two shower steps of a collinear QCD model. By exploiting the compact circuit architecture of the quantum walk, one can drastically reduce the quantum resources required to simulate a shower step. The second algorithm shows that, in this framework, the quantum parton shower can be extended to simulate realistic shower depths whilst using fewer quantum resources. Finally, the third algorithm utilises a discrete QCD approach to parton showering to include kinematics in the shower, simulating a dipole cascade. In this construction, the algorithm has achieved the first data comparison between synthetic data produced using a Noisy Intermediate-Scale Quantum (NISQ) device, and ``real-life" archival collider data from the Large Electron Positron collider. The three algorithms represent the development of quantum algorithms for the simulation of parton showers, acting as a first step towards a fully quantum simulation of a high energy collision event.Open Acces