Abstract
Let a program p on input a outputs b. We are looking for a shorter program p′ having the same property (p′(a)=b). In addition, we want p′ to be simple conditional to p (this means that the conditional Kolmogorov complexity K (p ′|p) is negligible). In the present paper, we prove that sometimes there is no such program p′, even in the case when the complexity of p is much bigger than K (b|a). We give three different constructions that use the game approach, probabilistic arguments and algebraic (combinatorial) arguments, respectively.
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References
Muchnik, A.A.: Conditional complexity and codes. Theoretical Computer Science 271, 97–109 (2002)
Muchnik, A., Ustinov, M.: Constructing non-reducible programs for given pair of strings (preprint)
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© 2006 Springer-Verlag Berlin Heidelberg
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Muchnik, A., Shen, A., Vereshchagin, N., Vyugin, M. (2006). Non-reducible Descriptions for Conditional Kolmogorov Complexity. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_29
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DOI: https://doi.org/10.1007/11750321_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
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