自然语言是一种外围过程吗？再论事实与文字定理
Is Natural Language a Perigraphic Process? The Theorem about Facts and Words Revisited
摘要：
正如我们所讨论的，一个平稳的随机过程是非遍历的，当一个随机的持久主题可以在从过程中采样的无限随机文本中检测到时，而我们称这个过程为强非遍历的，当一个无限序列的独立随机比特，称为概率事实，需要完全描述这个主题。替换概率事实与算法随机序列的位，称为算法的事实，我们适应这个属性回到遍历过程。随后，我们称一个进程为周图，如果可以从该进程中采样的有限文本中推断出的算法事实的数量像文本长度的幂一样增长。我们提出了这样一个过程的一个简单的例子。此外，我们证明了一个断言，我们称之为关于事实和文字的定理。这个命题指出，从一个过程中提取的文本中可以推断出的概率或算法事实的数量必须大致小于通过PPM压缩算法在该文本中检测到的不同单词状字符串的数量。我们还观察到，莎士比亚戏剧样本的单词字符串的数量遵循经验逐步幂律，与马尔可夫过程形成鲜明对比。因此，我们假设自然语言作为一个过程，不仅是非马尔可夫的，而且是循环的。
英文摘要：
As we discuss, a stationary stochastic process is nonergodic when a random persistent topic can be detected in the infinite random text sampled from the process, whereas we call the process strongly nonergodic when an infinite sequence of independent random bits, called probabilistic facts, is needed to describe this topic completely. Replacing probabilistic facts with an algorithmically random sequence of bits, called algorithmic facts, we adapt this property back to ergodic processes. Subsequently, we call a process perigraphic if the number of algorithmic facts which can be inferred from a finite text sampled from the process grows like a power of the text length. We present a simple example of such a process. Moreover, we demonstrate an assertion which we call the theorem about facts and words. This proposition states that the number of probabilistic or algorithmic facts which can be inferred from a text drawn from a process must be roughly smaller than the number of distinct word-like strings detected in this text by means of the PPM compression algorithm. We also observe that the number of the word-like strings for a sample of plays by Shakespeare follows an empirical stepwise power law, in a stark contrast to Markov processes. Hence we suppose that natural language considered as a process is not only non-Markov but also perigraphic.
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。
