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CSR
2009
Springer

Variations on Muchnik's Conditional Complexity Theorem

9 years 7 months ago
Variations on Muchnik's Conditional Complexity Theorem
Muchnik’s theorem about simple conditional descriptions states that for all strings a and b there exists a short program p transforming a to b that has the least possible length and is simple conditional on b. In this paper we present two new proofs of this theorem. The first one is based on the on-line matching algorithm for bipartite graphs. The second one, based on extractors, can be generalized to prove a version of Muchnik’s theorem for space-bounded Kolmogorov complexity. 1 Muchnik’s Theorem An. Muchnik [8] has proven the following theorem:
Daniil Musatov, Andrei E. Romashchenko, Alexander
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CSR
Authors Daniil Musatov, Andrei E. Romashchenko, Alexander Shen
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