Compression of enumerations and gain

04/06/2023

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by   George Barmpalias, et al.

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We study the compressibility of enumerations, and its role in the relative Kolmogorov complexity of computably enumerable sets, with respect to density. With respect to a strong and a weak form of compression, we examine the gain: the amount of auxiliary information embedded in the compressed enumeration. Strong compression and weak gainless compression is shown for any computably enumerable set, and a positional game is studied toward understanding strong gainless compression.