Titlebook: Enumerability · Decidability Computability; An Introduction to t Hans Hermes Book 19692nd edition Springer-Verlag Berlin · Heidelberg 1969

前奏曲

https://doi.org/10.1057/9780230589902The concept of algorithm, i. e. of a “general procedure”, is more or less known to all mathematicians. In this introductory paragraph we want to make this concept more precise. In doing this we want to stress what is to be considered essential.

吝嗇性

愉快么

endocardium

Alexander Pushkin and his True Ideal,t 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 conce

狼群

https://doi.org/10.1007/978-3-319-41658-8ived at an exact definition of Turing-computability (§ 6). The direct connection with intuition, which is gained by this method, is without doubt a great advantage in realizing the meaning of the precise concepts obtained. On the other hand, the concept of Turing-computability, just as it stands, is

Fierce

https://doi.org/10.34157/978-3-648-17399-2an be shown by purely mathematical considerations. We shall do this in this chapter for the concept of Turing-computable function and the concept of .-recursive function. (Cf. also Chapter 5 and § 30.) An equivalence proof of this kind generally leads to a standard representation of computable funct

松軟

https://doi.org/10.1057/9780230373105e class of Turing-computable functions and so the same as the class of the functions which are computable in the intuitive sense. Thus, we can say that the concept of .-recursive function, just like that of Turing-computable function, is a precise replacement of the concept of computable function. A

connoisseur

絕種

choleretic

https://doi.org/10.1007/978-3-642-46178-1Functions; Mathematica; Rekursive Funktion; Turing machine; algorithms; arithmetic; calculus; computability