Abstract
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.
Supported by ANR Sycomore, NAFIT ANR-08-EMER-008-01 and RFBR 09-01-00709-a grants.
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References
Musatov, D., Romashchenko, A., Shen, A.: Variations on Muchnik’s Conditional Complexity Theorem. Full version, http://arxiv.org/abs/0904.3116
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Musatov, D., Romashchenko, A., Shen, A. (2009). Variations on Muchnik’s Conditional Complexity Theorem. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_24
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DOI: https://doi.org/10.1007/978-3-642-03351-3_24
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