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Kolmogorov Complexity and the Recursion Theorem [PDF]
Transactions of the American Mathematical Society, 2006 Several classes of diagonally nonrecursive (DNR) functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A A
Bjørn Kjos-Hanssen +2 more
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Quantum Kolmogorov Complexity and Information-Disturbance Theorem
Entropy, 2011 In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vit´anyi has been examined. In the quantum information theory, the information-disturbance relationship, which treats
Takayuki Miyadera
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Increasing Kolmogorov Complexity [PDF]
, 2005 How much do we have to change a string to increase its Kolmogorov complexity? We show that we can increase the complexity of any non-random string of length n by flipping $O(\sqrt{n})$ bits and some strings require $\Omega(\sqrt{n})$ bit flips. For a given m, we also give bounds for increasing the complexity of a string by flipping m bits.
H.M. Buhrman (Harry) +3 more
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A Strange Application of Kolmogorov Complexity [PDF]
Theory of Computing Systems, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Hammer, Alexander Shen 0001
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Reductions to the set of random strings: The resource-bounded case [PDF]
Logical Methods in Computer Science, 2014 This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings.
Eric Allender +3 more
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SECOND QUANTIZED KOLMOGOROV COMPLEXITY [PDF]
International Journal of Quantum Information, 2008 The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantized Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties.
Rogers, C, Vedral, V, Nagarajan, R
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Complexity and the Emergence of Physical Properties
Entropy, 2014 Using the effective complexity measure, proposed by M. Gell-Mann and S. Lloyd, we give a quantitative definition of an emergent property. We use several previous results and properties of this particular information measure closely related to the random ...
Miguel Angel Fuentes
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Kolmogorov Complexity as a Language [PDF]
, 2011 The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where notions and statements that involve Kolmogorov complexity ...
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A Safe Approximation for Kolmogorov Complexity [PDF]
, 2014 Kolmogorov complexity (K) is an incomputable function. It can be approximated from above but not to arbitrary given precision and it cannot be approximated from below. By restricting the source of the data to a specific model class, we can construct a computable function κ¯ to approximate K in a probabilistic sense: the probability that the error is ...
Peter Bloem +4 more
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Kolmogorov compression complexity may differentiate different schools of Orthodox iconography
Scientific Reports, 2022 The complexity in the styles of 1200 Byzantine icons painted between 13th and 16th from Greece, Russia and Romania was investigated through the Kolmogorov algorithmic information theory. The aim was to identify specific quantitative patterns which define
Daniel Peptenatu +16 more
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