不可判定动力学的自指基础：从说谎者Parkman和停止问题到混沌的边缘
Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos
摘要：
在本文中，我们将探讨形式系统，算法和动力系统之间的几个基本关系，重点是不可判定性，普适性，对角化和自引用在这些计算框架中的作用。其中一些互连是众所周知的，而在本研究中澄清的递归形式系统，图灵机和元胞自动机（CA）之间的细粒度比较的结果。特别是，我们阐述了对角化参数应用于分布式计算进行CA，说明了哥德尔的CA证明的关键要素。比较分析强调了三个因素，其基础的能力，以产生不可判定的动态内检查的计算框架：（一）程序数据的二元性;（二）访问无限的计算介质的潜力;（三）实现否定的能力。哥德尔证明的修改区分了计算普适性和不可判定性，并展示了对角化论证如何在几个层面上利用不可判定性的自指基础。
英文摘要：
In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.
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