符号动力系统的可判定性与普适性
Decidability and Universality in Symbolic Dynamical Systems
摘要：
自图灵的工作以来，各种类型的动力系统的计算普适性的许多不同定义已经蓬勃发展。我们提出了一个普遍性的一般定义，适用于任意离散时间符号动力系统。系统的普适性定义为模型检验问题的不可判定性。对于图灵机、计数器机和标记系统，我们的定义与经典的定义一致。然而，它产生了一个新的定义细胞自动机和subshifts。我们的定义是强大的初始条件，这是一个理想的物理可实现的功能。我们推导出不可判定性和普适性的必要条件。例如，一个通用系统必须有一个敏感点和一个适当的子系统。我们猜想泛系统有无穷多个子系统。我们还讨论了论文，根据该计算应该发生在“混沌的边缘”，我们展示了一个普遍的混沌系统。
英文摘要：
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
