Affiliation:
1. Department of Mathematics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Abstract
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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