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

理解计算的极限对于推进计算机科学领域至关重要。

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

高效算法的开发既是一门艺术，也是一门科学。

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

P与NP问题是计算机科学中最重要的未解决问题之一。

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

多项式时间归约的概念对于理解NP完全问题的结构至关重要。

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

NP中的每个问题都可以归约为可满足性问题，这是计算复杂性理论的基石。

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

计算复杂性研究是通过数理逻辑和算法理论领域的旅程。

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

在计算的世界中，可能与不可能之间的界限通常由我们能够设计的算法定义。

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

算法的美在于它们能够解决乍一看似乎无法解决的问题。

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

NP完全性不仅仅是一个理论上的好奇心；它对实际计算有着深远的影响。

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

计算复杂性的本质是理解什么可以被有效地计算的极限。