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Synthetic Kolmogorov Complexity in Coq
International Conference on Interactive Theorem Proving, 2022 We present a generalised, constructive, and machine-checked approach to Kolmogorov complexity in the constructive type theory underlying the Coq proof assistant. By proving that nonrandom numbers form a simple predicate, we obtain elegant proofs of undecidability for random and nonrandom numbers and a proof of uncomputability of Kolmogorov complexity ...
Y. Forster, F. Kunze, Nils Lauermann
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Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures
Entropy, 2017 Turbulence is often expressed in terms of either irregular or random fluid flows, without quantification. In this paper, a methodology to evaluate the randomness of the turbulence using measures based on the Kolmogorov complexity (KC) is proposed.
Dragutin Mihailović +4 more
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The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning [PDF]
International Conference on Machine Learning, 2023 No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems.
Micah Goldblum +3 more
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Wave-Function Network Description and Kolmogorov Complexity of Quantum Many-Body Systems [PDF]
Physical Review X, 2023 Programmable quantum devices are now able to probe wave functions at unprecedented levels. This is based on the ability to project the many-body state of atom and qubit arrays onto a measurement basis which produces snapshots of the system wave function.
T. Mendes-Santos +10 more
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Topological Kolmogorov complexity and the Berezinskii-Kosterlitz-Thouless mechanism. [PDF]
Physical Review E, 2023 Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory to phases and excitations in quantum matter.
Vittorio Vitale +3 more
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Why Oatmeal is Cheap: Kolmogorov Complexity and Procedural Generation [PDF]
International Conference on Foundations of Digital Games, 2023 Although procedural generation is popular among game developers, academic research on the topic has primarily focused on new applications, with some research into empirical analysis.
Younès Rabii, Michael Cook
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Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity [PDF]
International Colloquium on Automata, Languages and Programming, 2022 The classical coding theorem in Kolmogorov complexity states that if an $n$-bit string $x$ is sampled with probability $\delta$ by an algorithm with prefix-free domain then K$(x) \leq \log(1/\delta) + O(1)$.
Zhenjian Lu, I. Oliveira, Marius Zimand
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Theory and Applications of Probabilistic Kolmogorov Complexity [PDF]
Electron. Colloquium Comput. Complex., 2022 Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of algorithms is a
Zhenjian Lu, I. Oliveira
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Quantum Kolmogorov complexity [PDF]
Proceedings 15th Annual IEEE Conference on Computational Complexity, 2001 14 pages, LaTeX2e, no figures, \usepackage{amssymb,a4wide}.
Berthiaume, A. +2 more
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List Approximation for Increasing Kolmogorov Complexity
Axioms, 2021 It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. However, is it possible to construct a few strings, no longer than the input string, so that most of them have larger complexity?
Marius Zimand
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