decidability

简明释义

英[dɪˈsaɪdəblɪti]美[dɪˈsaɪdəblɪti]

n. [数] 可判定性

英英释义

单词用法

同义词

反义词

例句

1.This thesis fully USES the expressing and reasoning ability of description logic and applies it in the spatial reasoning to increase the accuracy and decidability of the reasoning.

本论文将描述逻辑应用到空间推理中，充分利用描述逻辑较强的表达和推理能力，提高空间推理的准确性和可判定性。

2.This thesis fully USES the expressing and reasoning ability of description logic and applies it in the spatial reasoning to increase the accuracy and decidability of the reasoning.

本论文将描述逻辑应用到空间推理中，充分利用描述逻辑较强的表达和推理能力，提高空间推理的准确性和可判定性。

3.A model verification algorithm based on DTMA and the subset of DTMA modal logic is devised, and the decidability of the model verification is proved.

对于DTMA与DTMA模态逻辑的子集给出了一个模型验证的算法，证明了验证算法的可判定性。

4.This paper is devoted to a proof of decidability on consistent structure and gives a rapid decision method.

本文致力于相容结构的可判定性的证明并给出了一个快速的判定算法。

5.We present a dense timed interval temporal logic and exploit the decidability problem of DTITL.

定义了稠密时间区间时序逻辑，它是区间时序逻辑的一种实时扩充。

6.The decidability of the model is proven and a decidability algorithm is presented.

证明了该模型的可判定性，并给出了判定任意一个事件是否需要审计的算法。

7.The concept of algorithm is also used to define the notion of decidability.

算法的概念，也用来界定概念的决定性。

8.In computer science, the concept of decidability refers to whether a problem can be definitively solved by an algorithm.

在计算机科学中，可判定性的概念指的是一个问题是否可以通过算法被明确解决。

9.The decidability of certain logical statements is a key topic in mathematical logic.

某些逻辑语句的可判定性是数学逻辑中的一个关键主题。

10.Researchers are exploring the decidability of various types of formal languages.

研究人员正在探索各种形式语言的可判定性。

11.The famous Halting Problem is an example of a problem with undecidable decidability.

著名的停机问题是一个具有不可判定的可判定性的问题的例子。

12.Understanding decidability helps programmers know which problems can be solved efficiently.

理解可判定性可以帮助程序员了解哪些问题可以高效解决。

作文

In the realm of computer science and mathematics, the concept of decidability plays a crucial role in understanding the limits of computation and algorithmic processes. Decidability refers to the ability to determine, through a finite procedure, whether a given statement or problem is true or false. This concept is particularly significant in the study of formal languages, logic, and the theory of computation. To elaborate, a problem is said to be decidable if there exists an algorithm that can provide a yes or no answer for every instance of the problem within a finite amount of time. For example, the problem of determining whether a given number is prime is decidable because there are algorithms that can accomplish this task efficiently. In contrast, some problems are classified as undecidable, meaning that no such algorithm exists. A classic example of an undecidable problem is the Halting Problem, which asks whether a given program will eventually halt or run indefinitely. Alan Turing proved that there is no general algorithm that can solve this problem for all possible program-input pairs, illustrating the limitations of computation. Understanding decidability is essential not only for theoretical computer scientists but also for practitioners who design algorithms and software. When faced with a computational problem, recognizing whether it is decidable can influence the approach taken to find a solution. If a problem is decidable, one can invest time and resources into developing an effective algorithm. However, if a problem is undecidable, efforts may be better spent on approximations or heuristics, as no exact solution exists. The implications of decidability extend beyond pure mathematics and computer science; they touch upon philosophy, particularly in the realms of logic and epistemology. The question of what can be known or proven often mirrors the questions of decidability. For example, in formal systems, certain statements may be true but unprovable, leading to discussions about the nature of truth and knowledge. Gödel's incompleteness theorems, which demonstrate inherent limitations in formal systems, are deeply connected to the notion of decidability. Moreover, the exploration of decidability has practical applications in various fields, including artificial intelligence, programming languages, and even legal reasoning. In AI, understanding which problems are decidable can help in building systems that can reason effectively about certain domains. In programming languages, decidability issues arise when determining properties such as type checking or program equivalence. Legal reasoning can also benefit from insights into decidability, as legal systems often grapple with the complexities of rules and interpretations that may or may not yield clear decisions. In conclusion, the concept of decidability is foundational to many areas of study and has far-reaching implications. It helps delineate the boundaries of what can be computed or solved algorithmically. By grasping the significance of decidability, we gain invaluable insights into the capabilities and limitations of both machines and human reasoning. As we continue to advance in technology and theoretical understanding, the exploration of decidability will remain a vital part of our intellectual journey, guiding us in our quest for knowledge and understanding in a complex world.

在计算机科学和数学领域，可判定性的概念在理解计算和算法过程的限制方面起着至关重要的作用。可判定性是指通过有限的程序确定给定语句或问题是真还是假的能力。这个概念在形式语言、逻辑和计算理论的研究中尤为重要。 具体来说，如果存在一个算法可以在有限时间内为问题的每个实例提供是或否的答案，则该问题被称为可判定的。例如，判断一个给定数字是否为质数的问题是可判定的，因为有算法可以有效地完成这一任务。相反，有些问题被归类为不可判定，这意味着不存在这样的算法。一个经典的不可判定问题是停机问题，它询问给定程序是否最终会停止或无限运行。艾伦·图灵证明，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，这说明了计算的局限性。 理解可判定性对理论计算机科学家和设计算法及软件的从业者都至关重要。在面对计算问题时，认识到它是否是可判定的可以影响找到解决方案的方法。如果一个问题是可判定的，可以投入时间和资源来开发有效的算法。然而，如果一个问题是不可判定的，努力可能更好地集中在近似或启发式方法上，因为不存在精确的解决方案。 可判定性的影响不仅扩展到纯数学和计算机科学，还涉及哲学，特别是在逻辑和认识论领域。关于什么可以被知道或证明的问题往往与可判定性的问题相呼应。例如，在形式系统中，某些陈述可能是真的但不可证明，从而引发关于真理和知识本质的讨论。哥德尔的不完全性定理展示了形式系统中的固有限制，与可判定性的概念密切相关。 此外，对可判定性的探索在多个领域具有实际应用，包括人工智能、编程语言甚至法律推理。在人工智能中，理解哪些问题是可判定的可以帮助构建能够有效推理某些领域的系统。在编程语言中，当确定类型检查或程序等价性等属性时，会出现可判定性问题。法律推理也可以从可判定性的见解中受益，因为法律系统常常面临规则和解释的复杂性，这些规则和解释可能无法明确决策。 总之，可判定性的概念是许多研究领域的基础，并具有深远的影响。它有助于划定可以通过算法计算或解决的边界。通过掌握可判定性的重要性，我们获得了对机器和人类推理的能力和局限性的宝贵见解。随着我们在技术和理论理解上的不断进步，对可判定性的探索将继续成为我们智力旅程的重要组成部分，引导我们在复杂世界中追求知识和理解的过程中。