理查德·卡普
計(jì)算復(fù)雜性理論的奠基人
Understanding the limits of computation is essential for advancing the field of computer science.
理解計(jì)算的極限對(duì)于推進(jìn)計(jì)算機(jī)科學(xué)領(lǐng)域至關(guān)重要。
The development of efficient algorithms is as much an art as it is a science.
高效算法的開(kāi)發(fā)既是一門(mén)藝術(shù)，也是一門(mén)科學(xué)。
The P versus NP problem is one of the most important unsolved problems in computer science.
P與NP問(wèn)題是計(jì)算機(jī)科學(xué)中最重要的未解決問(wèn)題之一。
The concept of polynomial-time reduction is central to understanding the structure of NP-complete problems.
多項(xiàng)式時(shí)間歸約的概念對(duì)于理解NP完全問(wèn)題的結(jié)構(gòu)至關(guān)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(gè)問(wèn)題都可以歸約為可滿(mǎn)足性問(wèn)題，這是計(jì)算復(fù)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(jì)算復(fù)雜性研究是通過(guò)數(shù)理邏輯和算法理論領(lǐng)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(jì)算的世界中，可能與不可能之間的界限通常由我們能夠設(shè)計(jì)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(wú)法解決的問(wèn)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(gè)理論上的好奇心；它對(duì)實(shí)際計(jì)算有著深遠(yuǎn)的影響。
The essence of computational complexity is to understand the limits of what can be computed efficiently.
計(jì)算復(fù)雜性的本質(zhì)是理解什么可以被有效地計(jì)算的極限。