Computability of Recursive Functions
Journal of the ACM (JACM)
Words in the History of a Turing Machine with a Fixed Input
Journal of the ACM (JACM)
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Further Results on the Problem of Finding Minimal Length Programs for Decision Tables
Journal of the ACM (JACM)
On the problem of communicating complex information
Communications of the ACM
An analysis of optimal control system algorithms
AFIPS '72 (Fall, part I) Proceedings of the December 5-7, 1972, fall joint computer conference, part I
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A definition is given of the efficiency of an algorithm considered as a whole. This immediately raises the question of whether it is possible to find the most efficient or “optimum” algorithm. It is shown that an optimization problem of this kind is effectively solvable if and only if the set of arguments with which one is concerned is a finite one. Next, conditions under which an optimum algorithm does or does not exist are considered, and a limiting recursive process for finding it when it does is produced. Finally, some observations are made about the best space-time measure for algorithms which can be expected in certain cases. The results and proofs are couched in terms of Turing machines but may be adapted without difficulty to apply to other infinite digital machines such as the extensions of actual computers obtained by adding an infinite memory, or to the computations involved in other theoretical formulations of partial recursive functions such as those provided by Kleene's systems of equations or the URM's of Shepherdson and Sturgis.