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The Computer Journal 1999 42(4):284-286; doi:10.1093/comjnl/42.4.284
© 1999 by British Computer Society
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Robust Measures of Information

Leonid. A. LevinA1

A1 Computer Science Department, Boston University, 111 Cummington Street, Boston, MA 02215, USA Email: Lnd@bu.edu A2 An earlier version was presented in FOCS-1988.

The usual (i.e. easily computable) probability distributions share a remarkable feature. They are concentrated on strings which do not differ noticeably in any robust characteristic, except their informational size (Kolmogorov complexity). The formalization of this statement (below) distinguishes a class of homogeneous probability measures suggesting various applications. In particular, it may explain why the average case NP-completeness results are so measure-independent and may lead to their generalization to this wider and more invariant class of measures. It also demonstrates a sharp difference between the pseudorandom strings and the objects known before.


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