“effective computability”的概念、定义、翻译、参考文献-科学参考

effective computability

Computer

Let
$\begin{array}{l} N = {0, 1, \dots} \\ \begin{array}{l} N^{k} = N \times \dots \times N \\ (with k factors) \end{array} \end{array}$
A partial function
$f : N^{k} \to N$
is effectively computable if there is an effective procedure or algorithm that correctly calculates f. An effective procedure is one that meets the following specifications. Firstly, the procedure must consist of a finite set of ‘simple’ instructions and there must be no ambiguity concerning the order in which the instructions are to be carried out. Secondly, if the procedure is given a k-tuple x in the domain of f, then after a finite number of steps, the calculation must terminate and output f(x); if the procedure is given a k-tuple not in the domain of f it must not output a value. See also Church–Turing thesis.

单词	effective computability
释义	effective computability Computer Let $\begin{array}{l} N = {0, 1, \dots} \\ \begin{array}{l} N^{k} = N \times \dots \times N \\ (with k factors) \end{array} \end{array}$ A partial function $f : N^{k} \to N$ is effectively computable if there is an effective procedure or algorithm that correctly calculates f. An effective procedure is one that meets the following specifications. Firstly, the procedure must consist of a finite set of ‘simple’ instructions and there must be no ambiguity concerning the order in which the instructions are to be carried out. Secondly, if the procedure is given a k-tuple x in the domain of f, then after a finite number of steps, the calculation must terminate and output f(x); if the procedure is given a k-tuple not in the domain of f it must not output a value. See also Church–Turing thesis.
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