The generalized Kolmogorov complexity of sets

Recent work has shown that it is useful to consider new variants of time-bounded Kolmogorov complexity. The author reviews that work, presents the new definitions, and studies the basic properties of these measures. He deals with the function K/sub L/, which measures the complexity of the simplest strings in the language L and with sets of the form KU/sub v/(s(n),t(n)), which consists of strings with unique short descriptions.<
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