论语法代码的词汇与文本的逻辑一致性
On the Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts
摘要：
本文从信息论的两个方面对自然语言中的Zipf-Mandelbrot定律作了新的解释。首先，我们构造了一类新的基于文法的码，其次，我们研究了强非遍历平稳过程的性质。共同讨论的动机是用一个简单的非正式陈述来证明一个命题：如果一个长度为$n$的文本以重复的方式描述$n^β$独立的事实，那么在$n$上的适当条件下，该文本至少包含$n^β/\log n$不同的词。在形式陈述中，采用了两个建模假设。首先，单词被理解为文本的最短基于语法的编码的非终结符符号。其次，文本被假定为是由一个有限能量强非遍历源，而事实是二进制IID变量可预测的移位不变的方式。
英文摘要：
The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to prove a proposition with a simple informal statement: If a text of length $n$ describes $n^β$ independent facts in a repetitive way then the text contains at least $n^β/\log n$ different words, under suitable conditions on $n$. In the formal statement, two modeling postulates are adopted. Firstly, the words are understood as nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the text is assumed to be emitted by a finite-energy strongly nonergodic source whereas the facts are binary IID variables predictable in a shift-invariant way.
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。
