Stability of properties of Kolmogorov complexity under relativization

Stability of properties of Kolmogorov complexity under relativization Assume that a tuple of binary strings $$ \bar a $$ = ⟨a 1 ..., a n ⟩ has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of $$ \bar a $$ do not change significantly if we relativize them to b? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an ∃-formula). In particular, we show that a random (conditional on $$ \bar a $$ ) oracle b does not help to extract common information from the strings a i . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Stability of properties of Kolmogorov complexity under relativization

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946010010059
Publisher site
See Article on Publisher Site

Abstract

Assume that a tuple of binary strings $$ \bar a $$ = ⟨a 1 ..., a n ⟩ has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of $$ \bar a $$ do not change significantly if we relativize them to b? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an ∃-formula). In particular, we show that a random (conditional on $$ \bar a $$ ) oracle b does not help to extract common information from the strings a i .

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 23, 2010

References

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