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- Chain_rule_for_Kolmogorov_complexity abstract "The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states:That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.This follows immediately from the definitions of conditional and joint entropy fact from probability theory that the joint probability is the product of the marginal and conditional probability:The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:(An exact version, KP(x, y) = KP(x) + KP(y|x*) + O(1),holds for the prefix complexity KP, where x* is a shortest program for x.)It states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor. The results implies that algorithmic mutual information, an analogue of mutual information for Kolmogorov complexity is symmetric: I(x:y) = I(y:x) + O(log K(x,y)) for all x,y.".
- Chain_rule_for_Kolmogorov_complexity wikiPageID "8566056".
- Chain_rule_for_Kolmogorov_complexity wikiPageRevisionID "593705018".
- Chain_rule_for_Kolmogorov_complexity hasPhotoCollection Chain_rule_for_Kolmogorov_complexity.
- Chain_rule_for_Kolmogorov_complexity subject Category:Algorithmic_information_theory.
- Chain_rule_for_Kolmogorov_complexity subject Category:Articles_containing_proofs.
- Chain_rule_for_Kolmogorov_complexity subject Category:Computability_theory.
- Chain_rule_for_Kolmogorov_complexity subject Category:Information_theory.
- Chain_rule_for_Kolmogorov_complexity subject Category:Theory_of_computation.
- Chain_rule_for_Kolmogorov_complexity comment "The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states:That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.This follows immediately from the definitions of conditional and joint entropy fact from probability theory that the joint probability is the product of the marginal and conditional probability:The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:(An exact version, KP(x, y) = KP(x) + KP(y|x*) + O(1),holds for the prefix complexity KP, where x* is a shortest program for x.)It states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor. ".
- Chain_rule_for_Kolmogorov_complexity label "Chain rule for Kolmogorov complexity".
- Chain_rule_for_Kolmogorov_complexity sameAs m.02783s5.
- Chain_rule_for_Kolmogorov_complexity sameAs Q5067959.
- Chain_rule_for_Kolmogorov_complexity sameAs Q5067959.
- Chain_rule_for_Kolmogorov_complexity wasDerivedFrom Chain_rule_for_Kolmogorov_complexity?oldid=593705018.
- Chain_rule_for_Kolmogorov_complexity isPrimaryTopicOf Chain_rule_for_Kolmogorov_complexity.