V2EX halting problem

Halting Problem

释义 / Definition

“停机问题”:计算理论中的经典问题给定一个程序(或图灵机)和输入,判断该程序是否会在有限步内停止并输出结果,还是会无限运行。图灵证明:不存在一个对所有程序与输入都能正确判断的通用算法(该问题在一般情况下是不可判定的)。(在某些受限情形下可判定。)

发音 / Pronunciation

/hlt prblm/

例句 / Examples

The halting problem shows that some questions cannot be solved by any algorithm.
停机问题表明,有些问题无法用任何算法彻底解决。

Researchers often reduce a new undecidable problem to the halting problem to prove it has no general solution.
研究者常把一个新的不可判定问题归约到停机问题上,以证明它不存在通用解法。

词源 / Etymology

“Halting”来自动词 halt(停止、终止运行),与“程序停止执行”这一含义直接相关;“problem”指数学或理论计算机科学中的“问题”。该术语因艾伦图灵在1936年的工作而广为人知,成为“可计算性/不可判定性”研究的核心概念之一。

相关词 / Related Words

文学与名著用例 / Notable Works

  • Alan Turing, On Computable Numbers, with an Application to the Entscheidungsproblem(1936)
  • Douglas R. Hofstadter, Gdel, Escher, Bach: An Eternal Golden Braid(书中讨论可计算性与不可判定性时涉及停机问题)
  • Michael Sipser, Introduction to the Theory of Computation(以停机问题作为不可判定性的核心例子)
  • Martin Davis, Computability and Unsolvability(系统讨论停机问题与相关结果)
  • Charles Petzold, The Annotated Turing(对图灵论文与停机问题的通俗注解)
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