Glass网络的熵界
Entropy bounds for Glass networks
AI总结：
该研究提出混沌Glass网络是真随机数生成器的良好候选，开发了计算其熵上界的程序并改进现有结果，验证了该方法能通过少量细化步骤接近真实熵，为网络不规则性评估提供理论手段。
摘要：
我们提出混沌Glass网络（一类分段线性常微分方程）是真随机数生成器设计的良好候选。Glass网络设计的优势在于仅涉及标准布尔逻辑门。此外，已混沌（确定性）系统结合热噪声导致的随机“抖动”，能以比噪声极限环振荡器更稳健的方式生成随机比特序列。由于目标是生成具有尽可能大正熵的比特序列，因此需要一种理论方法来评估一大类网络的不规则性。我们在此开发了一种通过连续动力学的符号表示来计算Glass网络熵的良好上界的程序。我们的方法改进了Farcot（2006）的结果，原则上通过细化估计可达到任意精度，并表明在极限情况下，这些估计收敛于对应连续动力学符号系统的真实熵。作为对该方法的验证，我们展示了对一个示例网络，仅经过几步细化后的上界就非常接近从长期数值模拟估计的熵。
英文摘要：
We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard Boolean logic gates. Furthermore, an already chaotic (deterministic) system combined with random ``jitter'' due to thermal noise can be used to generate random bit sequences in a more robust way than noisy limit-cycle oscillators. Since the goal is to generate bit sequences with as large a positive entropy as possible, it is desirable to have a theoretical method to assess the irregularity of a large class of networks. We develop a procedure here to calculate good upper bounds on the entropy of a Glass network, by means of symbolic representations of the continuous dynamics. Our method improves on a result by Farcot (2006), and allows in principle for an arbitrary level of precision by refinements of the estimate, and we show that in the limiting case, these estimates converge to the true entropy of the symbolic system corresponding to the continuous dynamics. As a check on the method, we demonstrate for an example network that our upper bound after only a few refinement steps is very close to the entropy estimated from a long numerical simulation.
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