Related papers: Why Oatmeal is Cheap: Kolmogorov Complexity and Pr…
The Kolmogorov complexity of the word w is equal to the length of the shortest concatenation of program Z and its input x with which the word w is computed by the universal turing machine U. The question introduced in this paper is the…
Artificial Intelligence (AI)-driven material design has been attracting great attentions as a groundbreaking technology across a wide spectrum of industries. Molecular design is particularly important owing to its broad application domains…
This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…
Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that…
We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple…
Human creativity is often described as the mental process of combining associative elements into a new form, but emerging computational creativity algorithms may not operate in this manner. Here we develop an inverse problem formulation to…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…
LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help…
Interactive fictions, or text-adventures, are games in which a player interacts with a world entirely through textual descriptions and text actions. Text-adventure games are typically structured as puzzles or quests wherein the player must…
An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov…
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these…
The design of crystal materials plays a critical role in areas such as new energy development, biomedical engineering, and semiconductors. Recent advances in data-driven methods have enabled the generation of diverse crystal structures.…
A method of random search based on Kolmogorov complexity is proposed and applied to two search problems in group theory. The method is provably effective but not practical, so the applications involve heuristic approximations. Perhaps…
The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this…
A link between Kolmogorov Complexity and geometry is uncovered. A similar concept of projection and vector decomposition is described for Kolmogorov Complexity. By using a simple approximation to the Kolmogorov Complexity, coded in…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
Human collaboration with systems within the Computational Creativity (CC) field is often restricted to shallow interactions, where the creative processes, of systems and humans alike, are carried out in isolation, without any (or little)…