In this chapter the concept of Turing machine will be introduced without the heuristic considerations of the last chapter. Moreover, the most important constructive concepts, which we have already come across in Chapter 1, will be defined by Turing machines. We should convince ourselves that the suggested definitions of Turing-decidability, Turing-computability and Turing-enumerability are precise replacements of the corresponding intuitive concepts. These definitions can be considered to be really obvious if we agree that the Turing machines represent a legitimate precise substitute for the concept of algorithm. In the end we shall give an account of a few simple examples of Turing machines. The machines a i, r and L introduced in §6.5 are fundamentally important.
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