非常简单的混凝土浇筑机AIT
Very Simple Chaitin Machines for Concrete AIT
摘要：
1975年，柴廷提出了他著名的欧米茄数，即普适柴廷机的停机概率，这是一种具有无前缀域的普适图灵机。欧米茄数的位是{ \em算法上随机的}--如果我们将“原因”定义为比数据本身更小的可计算解释，那么位就没有理由是它们的样子。从那时起，只有{ \em two}显式通用Chaitin机被提出，都是Chaitin自己提出的。具体的算法信息论涉及到对特定的通用图灵机的研究，人们可以用特定的数值界限来陈述定理，而不是包括像O（1）这样的术语。我们提出了几个新的小Chaitin机（那些前缀自由域）适合于具体的算法信息论的研究。其中一台机器，我们称之为Keraia，是基于curried lambda运算符的λ演算的二进制编码。源代码包含在附录中。我们还给出了一个算法，用于限制域的空白结束标记机的前缀自由域的字母表，不包括结束标记，这使得人们可以采取许多通用的图灵机，并从它们构建通用Chaitin机。
英文摘要：
In 1975, Chaitin introduced his celebrated Omega number, the halting probability of a universal Chaitin machine, a universal Turing machine with a prefix-free domain. The Omega number's bits are {\em algorithmically random}--there is no reason the bits should be the way they are, if we define ``reason'' to be a computable explanation smaller than the data itself. Since that time, only {\em two} explicit universal Chaitin machines have been proposed, both by Chaitin himself. Concrete algorithmic information theory involves the study of particular universal Turing machines, about which one can state theorems with specific numerical bounds, rather than include terms like O(1). We present several new tiny Chaitin machines (those with a prefix-free domain) suitable for the study of concrete algorithmic information theory. One of the machines, which we call Keraia, is a binary encoding of lambda calculus based on a curried lambda operator. Source code is included in the appendices. We also give an algorithm for restricting the domain of blank-endmarker machines to a prefix-free domain over an alphabet that does not include the endmarker; this allows one to take many universal Turing machines and construct universal Chaitin machines from them.
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。
