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Compression of enumerations and gain (2304.03030v1)
Published 6 Apr 2023 in cs.CL, cs.IT, math.IT, and math.LO
Abstract: 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.