Homogeneous measures and polynomial time invariants

Authors:
L. A. Levin
Affiliations:
Dept. of Comput. Sci., Boston Univ., MA, USA
Venue:
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Year:
1988

Citing 0
Cited 3

On the existence of pseudorandom generators

CRYPTO '88 Proceedings on Advances in cryptology
Sparse pseudorandom distributions (extended abstract)

CRYPTO '89 Proceedings on Advances in cryptology
Notes on Levin's theory of average-case complexity

Studies in complexity and cryptography

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Abstract

The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completeness results are so measure-independent and could lead to their generalization to this wider and more invariant class of measures. It also demonstrates a sharp difference between recently discovered pseudorandom strings and the objects known before.