LT ^2C^2：一种具有图灵可计算柯尔莫哥洛夫复杂性的思维语言
LT^2C^2: A language of thought with Turing-computable Kolmogorov complexity
摘要：
在本文中，我们提出了一种理论上的努力，通过实现一种具体的思维语言，将程序大小理论与心理学联系起来，这种思维语言具有满足以下要求的图灵可计算柯尔莫哥洛夫复杂性（LT^2C^2）：1）足够简单，使得可以计算任何给定的有限二进制序列的复杂度，2）基于人类推理的有形操作（打印，重复，.），3)足够强大以产生所有可能的序列，但不太强大以识别人类不可见的序列。我们首先形式化LT^2C^2，给出它的语法和语义，并定义了一个适当的程序大小的概念。我们的设置导致了一个相对于LT^2C^2的柯尔莫哥洛夫复杂度函数，它可以在多项式时间内计算，并且它还在所罗门诺夫归纳推理理论的精神下导出了一个预测算法。然后，我们证明了这种语言的有效性，通过调查参与者试图生成随机字符串产生的字符串。参与者对随机性有深刻的理解，因此避免了典型的误解，如夸大交替的数量。我们推断，剩余的“记忆”将表达人类思想的算法本质，以特定模式的形式展现出来。相对于LT^2C^2的柯尔莫哥洛夫复杂度通过了三个预期的检验：1）人类序列的复杂度低于对照PRNG序列; 2）人类序列不是稳定的，显示出疲劳导致的复杂度降低; 3）每个个体都显示出算法稳定性的痕迹，因为部分序列的拟合比平均拟合更有效地预测后续序列。这项工作扩展了以前的努力，结合概念的柯尔莫哥洛夫复杂性理论和算法信息理论的心理学，明确.
英文摘要：
In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2) satisfying the following requirements: 1) to be simple enough so that the complexity of any given finite binary sequence can be computed, 2) to be based on tangible operations of human reasoning (printing, repeating,...), 3) to be sufficiently powerful to generate all possible sequences but not too powerful as to identify regularities which would be invisible to humans. We first formalize LT^2C^2, giving its syntax and semantics and defining an adequate notion of program size. Our setting leads to a Kolmogorov complexity function relative to LT^2C^2 which is computable in polynomial time, and it also induces a prediction algorithm in the spirit of Solomonoff's inductive inference theory. We then prove the efficacy of this language by investigating regularities in strings produced by participants attempting to generate random strings. Participants had a profound understanding of randomness and hence avoided typical misconceptions such as exaggerating the number of alternations. We reasoned that remaining regularities would express the algorithmic nature of human thoughts, revealed in the form of specific patterns. Kolmogorov complexity relative to LT^2C^2 passed three expected tests examined here: 1) human sequences were less complex than control PRNG sequences, 2) human sequences were not stationary, showing decreasing values of complexity resulting from fatigue, 3) each individual showed traces of algorithmic stability since fitting of partial sequences was more effective to predict subsequent sequences than average fits. This work extends on previous efforts to combine notions of Kolmogorov complexity theory and algorithmic information theory to psychology, by explicitly ...
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