undecidable

简明释义

英[ˌʌndɪˈsaɪdəbəl]美[ˌʌndɪˈsaɪdəbəl]

adj. [数] 不可判定的

英英释义

单词用法

同义词

反义词

例句

1.Because precise determination of a computer virus is undecidable, a method based on improved K-nearest neighbor to detect computer virus approximately is presented in this paper.

由于计算机病毒检测的不可判定性，提出了一种基于改进的K最近邻检测方法来实现对计算机病毒的近似判别。

2.This theorem reveals that there exist undecidable propositions in a consistent formal system.

该定理揭示了在一个相容形式系统中存在着不可判定的命题。

3.Because precise determination of a computer virus is undecidable, a method based on improved K-nearest neighbor to detect computer virus approximately is presented in this paper.

由于计算机病毒检测的不可判定性，提出了一种基于改进的K最近邻检测方法来实现对计算机病毒的近似判别。

4.An undecidable statement can be thought of as a mathematical form of a statement like "I always lie."

一个无法判定的命题可以被当成是“我总是说谎”的数学形式。

5.In logic, the status of certain statements may remain undecidable 不可判定的 based on the axioms chosen.

在逻辑中，某些陈述的状态可能根据所选公理保持不可判定的。

6.The concept of undecidable 不可判定的 propositions is fundamental in Gödel's incompleteness theorems.

在哥德尔的不完备定理中，不可判定的命题概念是基础。

7.The question of whether a given program will halt is an undecidable 不可判定的 problem in computer science.

判断一个给定程序是否会停止是计算机科学中的一个不可判定的问题。

8.In computational theory, some problems are proven to be undecidable 不可判定的, meaning no algorithm can determine their truth value.

在计算理论中，有些问题被证明是不可判定的，这意味着没有算法可以确定它们的真值。

9.Many mathematicians encounter undecidable 不可判定的 statements that cannot be proven or disproven within a given axiomatic system.

许多数学家遇到的不可判定的命题在给定公理系统内无法被证明或反驳。

作文

In the realm of mathematics and logic, the concept of undecidable problems plays a crucial role in understanding the limits of what can be computed or proven. An undecidable problem is one for which no algorithm can be constructed that will always lead to a correct yes-or-no answer. This notion was famously illustrated by Kurt Gödel's incompleteness theorems, which demonstrated that within any sufficiently powerful logical system, there exist statements that are true but cannot be proven within that system. For instance, consider the Halting Problem, which asks whether a given program will eventually halt or run indefinitely. Alan Turing proved that there is no general algorithm to solve this problem for all possible program-input pairs, thus categorizing it as undecidable.Understanding undecidable problems is not just an academic exercise; it has practical implications in computer science, particularly in fields like artificial intelligence and software development. When we encounter a problem that is undecidable, it means that we must approach it with caution, recognizing that our computational methods may not yield definitive results. This awareness can guide developers in designing systems that account for uncertainty and incomplete information.Moreover, the existence of undecidable problems raises philosophical questions about the nature of knowledge and truth. If there are truths that are inherently undecidable, what does that imply about our understanding of the universe? It suggests that there may always be limits to human comprehension and that some questions may forever remain beyond our grasp. This perspective can be both humbling and motivating, encouraging further inquiry while acknowledging the boundaries of our current knowledge.In the context of decision-making, encountering undecidable situations can lead to significant challenges. For example, in legal contexts, certain cases may present undecidable dilemmas where the application of law does not yield a clear outcome. Judges and juries often face such complexities, requiring them to rely on principles, precedents, and moral reasoning rather than definitive answers. This highlights the importance of critical thinking and ethical considerations in navigating undecidable scenarios.In conclusion, the term undecidable encapsulates a profound aspect of both theoretical and practical domains. It signifies the boundaries of computation, the philosophical implications of knowledge, and the complexities of decision-making. As we continue to explore the vast landscape of mathematics, computer science, and philosophy, recognizing and embracing the undecidable will enable us to better understand the intricate tapestry of problems we face and the limits of our understanding. The journey through these undecidable territories challenges us to think critically, innovate, and remain open to the mysteries that lie ahead.

在数学和逻辑领域，undecidable（不可判定）问题的概念在理解计算或证明的极限方面发挥着重要作用。undecidable问题是指没有算法可以构造出总能给出正确的“是”或“否”答案的问题。这个概念通过库尔特·哥德尔的不完备性定理得到了著名的阐释，该定理表明，在任何足够强大的逻辑系统中，存在一些是真但无法在该系统内被证明的陈述。例如，考虑停机问题，它询问一个给定程序是否最终会停止或无限运行。艾伦·图灵证明了对于所有可能的程序输入对，没有通用算法可以解决这个问题，因此将其归类为undecidable。理解undecidable问题不仅仅是学术上的练习；它在计算机科学的实际应用中具有重要意义，特别是在人工智能和软件开发等领域。当我们遇到undecidable问题时，这意味着我们必须谨慎处理，认识到我们的计算方法可能无法得出明确的结果。这种意识可以指导开发人员设计能够考虑不确定性和不完整信息的系统。此外，undecidable问题的存在引发了关于知识和真理本质的哲学思考。如果存在固有的undecidable真理，那么这对我们对宇宙的理解意味着什么？这表明人类理解的界限可能永远存在，并且某些问题可能永远超出我们的掌握。这种观点既令人谦卑又激励人心，鼓励进一步探究，同时承认我们当前知识的边界。在决策的背景下，遇到undecidable情境可能会带来重大挑战。例如，在法律背景下，某些案件可能呈现出undecidable的困境，其中法律的适用并未产生明确的结果。法官和陪审团常常面临这样的复杂性，需要依赖原则、先例和道德推理，而不是明确的答案。这突显了在应对undecidable情境中批判性思维和伦理考量的重要性。总之，undecidable一词概括了理论和实践领域的深刻方面。它标志着计算的边界、知识的哲学意义以及决策的复杂性。随着我们继续探索数学、计算机科学和哲学的广阔领域，识别和接受undecidable将使我们更好地理解我们面临的复杂问题及我们理解的局限。穿越这些undecidable领域的旅程挑战我们进行批判性思考、创新，并保持对未来神秘事物的开放态度。