De Micco L, Larrondo H A, Plastino A, Rosso O A
Departamentos de Física y de Ingeniería Electrónica, Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata, Argentina.
Philos Trans A Math Phys Eng Sci. 2009 Aug 28;367(1901):3281-96. doi: 10.1098/rsta.2009.0075.
We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). 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: (i) which is the best PRNG among the available ones? and (ii) 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.
我们处理随机性量词，并专注于它们辨别与伪随机数生成器（PRNG）相关的时间序列中混沌特征的能力。该领域的研究人员因混沌映射实现简单而受激励将其用于生成PRNG。尽管存在非常有效的通用基准来测试PRNG，但我们认为此处提供的分析为混沌映射的主要统计特征，即（i）其不变测度和（ii）混合常数的重要性提供了额外的教学启示。这有助于回答应用中出现的两个问题：（i）现有PRNG中哪一个是最佳的？以及（ii）如果给定的PRNG结果不够好且仍必须对其应用随机化程序，哪种是最佳适用的随机化程序？我们的答案对现有文献中提出的几个量词进行了比较分析。
