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Computability and Randomness

André Nies

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic ... More


The descriptive complexity of strings

André Nies

in Computability and Randomness

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.003.0002
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops the theory of plain Kolmogorov complexity, and then of prefix-free Kolmogorov complexity. A main technical tool for later chapters is the Machine Existence (or Kraft–Chaitin) ... More


When are graphical causal models not good models?

Jan Lemeire, Kris Steenhaut, and Abdellah Touhafi

in Causality in the Sciences

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199574131
eISBN:
9780191728921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199574131.003.0027
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The principle of Kolmogorov minimal sufficient statistic (KMSS) states that the meaningful information of data is given by the regularities in the data. The KMSS is the minimal model that describes ... More


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