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Paper:

TR01-088 | 29th October 2001 00:00

Logical operations and Kolmogorov complexity

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TR01-088
Authors: Alexander Shen, Nikolay Vereshchagin
Publication: 28th November 2001 16:40
Downloads: 861
Keywords: 


Abstract:

We define Kolmogorov complexity of a set of strings as the minimal
Kolmogorov complexity of its element. Consider three logical
operations on sets going back to Kolmogorov
and Kleene:
(A OR B) is the direct sum of A,B,
(A AND B) is the cartesian product of A,B,
(A --> B) is the set of programs mapping
any element of A to an element of B.
We find complexity of certain
particular sets obtained from singelton sets (e.g. ({x}-->{y})-->{y}).




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