Abstract

to a practical application. A dozen years later the first stored-program electronic digital computers began to spring into existence. All were modelled on the universal Turing machine. Today's digital computers also are in essence universal Turing machines. 2. Is There a Known Upper Bound to Computability? Many textbooks on the fundamentals of computer science offer examples of informationprocessing tasks that are, it is claimed, absolutely uncomputable, in the sense that no machine can be specified to carry out these tasks. For example, it is said that no machine can repond to any given (finite) string of binary digits in accordance with the following rules: 3 (1) Answer '1' if the string is a program that will cause a universal Turing machine on whose tape it is inscribed to execute only a finite number of operations (such programs are called 'terminating'). (2) Answer '0' if the string is not a terminating program; i.e. if the st

Citations