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Register a new userQuantifiers for randomness of chaotic pseudo random number generators
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Added by
Hilda Angela Larrondo
Publication date
2008
fields
Physics
and research's language is
English
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We deal with randomness-quantifiers and concentrate on their ability do discern the hallmark of chaos in time-series used in connection with pseudo random number generators (PRNG). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely, i) its invariant measure and ii) the mixing constant. This is of help in answering two questions that arise in applications, that is, (1) which is the best PRNG among the available ones? and (2) If a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure?. Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.
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Excitable media are prevalent models for describing physical, chemical, and biological systems which support wave propagation. In this letter, we show that the time evolution of the medium state at the wave fronts can be determined by complicated chaotic attractors. Wave front dynamics can be controlled by initial data choice. Building on this groundwork, we show that there is a mechano-chemical analog of the Universal Turing machine for morphogenesis problems. Namely, a fixed mechano-chemical system can produce any prescribed cell pattern depending on its input (initial data). This universal mechanism uses fundamental physical effects: spontaneous symmetry breaking with formation of many interfaces (kinks), which interact non-locally via a fast diffusing reagent. This interaction creates chaos. We present algorithms allowing us to obtain a prescribed target cell pattern.
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and incomputability is a nontrivial task. We present the results of a search for algorithmic randomness and incomputability in the output from two different QRNGs, performed by applying tests based on the Solovay-Strassen test of primality and the Chaitin-Schwartz theorem. The first QRNG uses measurements of quantum vacuum fluctuations. The second QRNG is based on polarization measurements on entangled single photons; for this generator, we use looped (and thus highly compressible) strings that also allow us to assess the ability of the tests to detect repeated bit patterns. Compared to a previous search for algorithmic randomness, our study increases statistical power by almost 3 orders of magnitude.
In this work, we argue that the implications of Pseudo and Quantum Random Number Generators (PRNG and QRNG) inexplicably affect the performances and behaviours of various machine learning models that require a random input. These implications are yet to be explored in Soft Computing until this work. We use a CPU and a QPU to generate random numbers for multiple Machine Learning techniques. Random numbers are employed in the random initial weight distributions of Dense and Convolutional Neural Networks, in which results show a profound difference in learning patterns for the two. In 50 Dense Neural Networks (25 PRNG/25 QRNG), QRNG increases over PRNG for accent classification at +0.1%, and QRNG exceeded PRNG for mental state EEG classification by +2.82%. In 50 Convolutional Neural Networks (25 PRNG/25 QRNG), the MNIST and CIFAR-10 problems are benchmarked, in MNIST the QRNG experiences a higher starting accuracy than the PRNG but ultimately only exceeds it by 0.02%. In CIFAR-10, the QRNG outperforms PRNG by +0.92%. The n-random split of a Random Tree is enhanced towards and new Quantum Random Tree (QRT) model, which has differing classification abilities to its classical counterpart, 200 trees are trained and compared (100 PRNG/100 QRNG). Using the accent and EEG classification datasets, a QRT seemed inferior to a RT as it performed on average worse by -0.12%. This pattern is also seen in the EEG classification problem, where a QRT performs worse than a RT by -0.28%. Finally, the QRT is ensembled into a Quantum Random Forest (QRF), which also has a noticeable effect when compared to the standard Random Forest (RF)... ABSTRACT SHORTENED DUE TO ARXIV LIMIT
The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, statistical tests for RNGs are a mandatory part of cryptographic information protection systems, but their effectiveness is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source.
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