| M. Davis. Computatbility and Unsolvability. Dover, New York, N.Y., 1982. TU Vienna Project WOOP |
....we prove that the computational power of discrete loops with remainder functions is considerably great if we restrict our interest to applications which do not loop forever. Theorem 7.1. If the number of iterations of a general loop can be determined by an integer valued computable function [21] Phi, a discrete loop with a remainder function can be used to achieve the same effect. Proof. We define the remainder function of the discrete loop by r 1 : Phi; i.e. the number of iterations of the general loop r 1 : r Gamma 1: Clearly, after Phi iterations, r Phi = 0 and thus the ....
M. Davis. Computatbility and Unsolvability. Dover, New York, N.Y., 1982. TU Vienna Project WOOP
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