Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kolmogorov Complexity in perspective. Part II: Classification,
  Information Processing and Duality   We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.

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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph