V2EX decidability

Decidability

定义 Definition

decidability(可判定性):在数理逻辑与计算机科学中,指一个问题/命题是否存在总能在有限步骤内给出“是/否”答案的算法。常用于讨论某类问题是否“可由程序完全解决”。(也可泛指“是否可作出明确判断”的性质,但最常见的是技术含义。)

发音 Pronunciation (IPA)

/dsadblti/

例句 Examples

Decidability is a key topic in theoretical computer science.
可判定性是理论计算机科学中的一个关键主题。

The paper studies the decidability of whether a given formula is satisfiable under certain constraints.
这篇论文研究在特定约束下,判断给定公式是否可满足这一问题的可判定性。

词源 Etymology

来自 decidable(可判定的、可裁决的)+ 名词后缀 -ity(表示“性质、状态”)。decide 源自拉丁语 decidere,本义与“切断、了结”相关,后来引申为“做出决定、判定”。在现代逻辑与计算理论中,“decidable/decidability”专门用来描述“是否存在终止算法”的性质。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Michael Sipser, Introduction to the Theory of Computation(讨论可判定性、不可判定性与停机问题等核心概念)
  • H. R. Lewis & C. H. Papadimitriou, Elements of the Theory of Computation(系统介绍可判定性与计算理论)
  • George S. Boolos, John P. Burgess, Richard C. Jeffrey, Computability and Logic(将逻辑与可计算性联系起来,频繁使用“decidability”)
  • Douglas R. Hofstadter, Gdel, Escher, Bach: An Eternal Golden Braid(以通俗方式涉及逻辑、形式系统与可判定性/不可判定性的思想)
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