Universal computing systems. Part 1, Simulation of any Normal Algorithm by Turing machine. Part 2, A universal Turing machine to translate any Turing machine to a Normal Algorithm

Abstract

In this paper a direct, constructive proof of the equivalence of the Normal Algorithm and Turing machine using the Turing machines NAS (Normal Algorithm Simulator) and NAC (Normal Algorithm Converter) is presented. The Turing machine NAS can simulate any particular Normal Algorithm, and NAG can convert the quintuples of a given Turing machine to an equivalent Normal Algorithm.