Abstract
Is it possible to find a shortest description for a binary string? The well-known answer is “no, Kolmogorov complexity is not computable.” Faced with this barrier, one might instead seek a short list of candidates which includes a laconic description. Remarkably such approximations exist. This paper presents an efficient algorithm which generates a polynomial-size list containing an optimal description for a given input string. Along the way, we employ expander graphs and randomness dispersers to obtain an Explicit Online Matching Theorem for bipartite graphs and a refinement of Muchnik’s Conditional Complexity Theorem. Our main result extends recent work by Bauwens, Mahklin, Vereshchagin, and Zimand.
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Teutsch, J. Short lists for shortest descriptions in short time. comput. complex. 23, 565–583 (2014). https://doi.org/10.1007/s00037-014-0090-3
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DOI: https://doi.org/10.1007/s00037-014-0090-3
Keywords
- Kolmogorov complexity
- online matching
- bipartite expander graph
- disperser graph
- Muchnik’s Conditional Complexity Theorem