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Procedural Content Generation (PCG) is the algorithmic generation of content, often applied to games. PCG and PCG via Machine Learning (PCGML) have appeared in published games. However, it can prove difficult to apply these approaches in…

Artificial Intelligence · Computer Science 2023-09-26 Emily Halina , Matthew Guzdial

The evaluation of procedural content generation (PCG) systems for generating video game levels is a complex and contested topic. Ideally, the field would have access to robust, generalisable and widely accepted evaluation approaches that…

Human-Computer Interaction · Computer Science 2024-04-30 Oliver Withington , Michael Cook , Laurissa Tokarchuk

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of…

Computational Complexity · Computer Science 2017-03-08 Nikolai Vereshchagin , Alexander Shen

Compression is at the heart of intelligence. A theoretically optimal way to compress any sequence of data is to find the shortest program that outputs that sequence and then halts. However, such 'Kolmogorov compression' is uncomputable, and…

Computation and Language · Computer Science 2025-03-19 Ori Yoran , Kunhao Zheng , Fabian Gloeckle , Jonas Gehring , Gabriel Synnaeve , Taco Cohen

The attempt to utilize machine learning in PCG has been made in the past. In this survey paper, we investigate how generative artificial intelligence (AI), which saw a significant increase in interest in the mid-2010s, is being used for…

Artificial Intelligence · Computer Science 2024-07-15 Xinyu Mao , Wanli Yu , Kazunori D Yamada , Michael R. Zielewski

Kolmogorov complexity measures the algorithmic complexity of a finite binary string $\sigma$ in terms of the length of the shortest description $\sigma^*$ of $\sigma$. Traditionally, the length of a string is taken to measure the amount of…

Computational Complexity · Computer Science 2019-06-14 Cameron Fraize , Christopher P. Porter

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

History and Overview · Mathematics 2015-05-13 Alexander Shen

The aim of this paper is to study the relevance of simplicity and its formal representation as Kolmogorov or algorithmic complexity in the cognitive sciences. The discussion is based on two premises: 1) all human experience is generated in…

General Physics · Physics 2009-06-20 Giulio Ruffini

We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the…

Quantum Physics · Physics 2022-01-20 Alexei Kaltchenko

The ability to generate natural-language questions with controlled complexity levels is highly desirable as it further expands the applicability of question generation. In this paper, we propose an end-to-end neural complexity-controllable…

Computation and Language · Computer Science 2021-10-14 Sheng Bi , Xiya Cheng , Yuan-Fang Li , Lizhen Qu , Shirong Shen , Guilin Qi , Lu Pan , Yinlin Jiang

Procedural Level Generation via Machine Learning (PLGML), the study of generating game levels with machine learning, has received a large amount of recent academic attention. For certain measures these approaches have shown success at…

Artificial Intelligence · Computer Science 2018-09-26 Matthew Guzdial , Nicholas Liao , Mark Riedl

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov…

Statistical Mechanics · Physics 2018-02-14 J. Ruebeck , R. G. James , J. R. Mahoney , J. P. Crutchfield

We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results…

Computational Complexity · Computer Science 2025-12-30 Luke Tonon

The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation…

Logic · Mathematics 2010-03-25 Andrej A. Muchnik , Ilya Mezhirov , Alexander Shen , Nikolay Vereshchagin

With recent advances in large language models (LLMs), the concept of automatically generating children's educational materials has become increasingly realistic. Working toward the goal of age-appropriate simplicity in generated educational…

Computation and Language · Computer Science 2023-10-31 Maria Valentini , Jennifer Weber , Jesus Salcido , Téa Wright , Eliana Colunga , Katharina Kann

Given a set X of finite strings, one interesting question to ask is whether there exists a member of X which is simple conditional to all other members of X. Conditional simplicity is measured by low conditional Kolmogorov complexity. We…

Computational Complexity · Computer Science 2021-02-09 Samuel Epstein

Procedural Content Generation via Reinforcement Learning (PCGRL) offers a method for training controllable level designer agents without the need for human datasets, using metrics that serve as proxies for level quality as rewards. Existing…

Artificial Intelligence · Computer Science 2025-10-07 Sam Earle , Zehua Jiang , Eugene Vinitsky , Julian Togelius

Procedural content generation via machine learning (PCGML) is the process of procedurally generating game content using models trained on existing game content. PCGML methods can struggle to capture the true variance present in underlying…

Machine Learning · Computer Science 2021-07-28 Bowei Li , Ruohan Chen , Yuqing Xue , Ricky Wang , Wenwen Li , Matthew Guzdial

We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing…

Logic · Mathematics 2013-11-28 George Barmpalias , Angsheng Li

Kolmogorov complexity is the length of the ultimately compressed version of a file (that is, anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the…

Information Theory · Computer Science 2020-04-22 Paul Vitanyi