更改

跳到导航 跳到搜索
删除346字节 、 2021年7月28日 (三) 17:48
第591行: 第591行:  
早在1936年的论文中,图灵就对 "运动......完全由配置决定 "的 "自动机"和 "选择机 "进行了区分:
 
早在1936年的论文中,图灵就对 "运动......完全由配置决定 "的 "自动机"和 "选择机 "进行了区分:
   −
{{quote|...whose motion is only partially determined by the configuration ... When such a machine reaches one of these ambiguous configurations, it cannot go on until some arbitrary choice has been made by an external operator. This would be the case if we were using machines to deal with axiomatic systems.|''The Undecidable'', p. 118}}
     −
{{quote|...它的运动只是部分由配置决定…当这样一台机器达到其中一种不明确的配置时,它不能继续运行,直到外部操作者做出任意的选择。如果我们使用机器来处理公理系统,就会出现这种情况。
+
它的运动只是部分由配置决定…当这样一台机器达到其中一种不明确的配置时,它不能继续运行,直到外部操作者做出任意的选择。如果我们使用机器来处理公理系统,就会出现这种情况。
  ——The Undecidable,第118页
+
            ——The Undecidable,p.118
 +
 
   −
}}
      
Turing (1936) does not elaborate further except in a footnote in which he describes how to use an a-machine to "find all the provable formulae of the [Hilbert] calculus" rather than use a choice machine. He "suppose[s] that the choices are always between two possibilities 0 and 1. Each proof will then be determined by a sequence of choices i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>n</sub> (i<sub>1</sub> = 0 or 1, i<sub>2</sub> = 0 or 1, ..., i<sub>n</sub> = 0 or 1), and hence the number 2<sup>n</sup> + i<sub>1</sub>2<sup>n-1</sup> + i<sub>2</sub>2<sup>n-2</sup> + ... +i<sub>n</sub> completely determines the proof. The automatic machine carries out successively proof 1, proof 2, proof 3, ..." (Footnote ‡, The Undecidable, p.&nbsp;138)
 
Turing (1936) does not elaborate further except in a footnote in which he describes how to use an a-machine to "find all the provable formulae of the [Hilbert] calculus" rather than use a choice machine. He "suppose[s] that the choices are always between two possibilities 0 and 1. Each proof will then be determined by a sequence of choices i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>n</sub> (i<sub>1</sub> = 0 or 1, i<sub>2</sub> = 0 or 1, ..., i<sub>n</sub> = 0 or 1), and hence the number 2<sup>n</sup> + i<sub>1</sub>2<sup>n-1</sup> + i<sub>2</sub>2<sup>n-2</sup> + ... +i<sub>n</sub> completely determines the proof. The automatic machine carries out successively proof 1, proof 2, proof 3, ..." (Footnote ‡, The Undecidable, p.&nbsp;138)
150

个编辑

导航菜单