The number of steps required to compute a function depends, in general, on the type of computer that is used, on the choice of computer program, and on the input-output code. Nevertheless, the results obtained in this paper are so general as to be nearly independent of these considerations. A function is exhibited that requires an enormous number of steps to be computed, yet has a “nearly quickest” program: Any other program for this function, no matter how ingeniously designed it may be, takes practically as many steps as this nearly quickest program. A different function is exhibited with the property that no matter how fast a program may be for computing this function another program exists for computing the function very much faster. © 1967, ACM. All rights reserved.
CITATION STYLE
Blum, M. (1967). A Machine-Independent Theory of the Complexity of Recursive Functions. Journal of the ACM (JACM), 14(2), 322–336. https://doi.org/10.1145/321386.321395
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