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Understanding the limits of computation is essential for advancing the field of computer science.

理解計算的極限對于推進計算機科學領域至關重要。

The development of efficient algorithms is as much an art as it is a science.

高效算法的開發既是一門藝術，也是一門科學。

The P versus NP problem is one of the most important unsolved problems in computer science.

P與NP問題是計算機科學中最重要的未解決問題之一。

The concept of polynomial-time reduction is central to understanding the structure of NP-complete problems.

多項式時間歸約的概念對于理解NP完全問題的結構至關重要。

Every problem in NP can be reduced to the satisfiability problem, which is the cornerstone of computational complexity theory.

NP中的每個問題都可以歸約為可滿足性問題，這是計算復雜性理論的基石。

The study of computational complexity is a journey through the landscape of mathematical logic and algorithmic theory.

計算復雜性研究是通過數理邏輯和算法理論領域的旅程。

In the world of computing, the boundary between the possible and the impossible is often defined by the algorithms we can devise.

在計算的世界中，可能與不可能之間的界限通常由我們能夠設計的算法定義。

The beauty of algorithms lies in their ability to solve problems that seem insurmountable at first glance.

算法的美在于它們能夠解決乍一看似乎無法解決的問題。

NP-completeness is not just a theoretical curiosity; it has profound implications for practical computing.

NP完全性不僅僅是一個理論上的好奇心；它對實際計算有著深遠的影響。

The essence of computational complexity is to understand the limits of what can be computed efficiently.

計算復雜性的本質是理解什么可以被有效地計算的極限。