Titlebook: An Introduction to Kolmogorov Complexity and Its Applications; Ming Li,Paul Vitányi Textbook 19931st edition Springer Science+Business Med

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https://doi.org/10.1007/978-94-015-3302-7d be compared with the pidgeon hole principle or the probabilistic method. Whereas the older methods generally show the existence of an object with the required properties, the incompressibility argument shows that almost all objects have the required property. This follows immediately from the fact

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https://doi.org/10.1007/978-94-015-3265-5sing, and for application of complexity to physics issues. Physicists have used complexity arguments in a variety of settings like information distance, thermodynamics, chaos, biology, and philosophy. We touch briefly upon several themes, but focus on two main issues.

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Monographs in Computer Sciencehttp://image.papertrans.cn/a/image/155304.jpg

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0172-603X Overview: 978-1-4757-3860-5Series ISSN 0172-603X Series E-ISSN 2512-5486

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https://doi.org/10.1007/978-3-663-04666-0on should describe but one object. Prom among all descriptions of an object we can take the length of the shortest description as a measure of the object’s complexity. It is natural to call an object ‘simple’ if it has at least one short description, and to call it ‘complex’ if all of its descriptions are long.

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https://doi.org/10.1007/978-3-663-04666-0ticular type of .) rather than in relation to a set of objects from which the individual object may be selected. To do so, one could define the quantity of information in an object in terms of the number of bits required to describe it. A description of an object is evidently only useful if we can reconstruct the object from this description.