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理论
最终，一个理论的价值不在于它的复杂性，而在于它解释和预测的能力。
In the end, the value of a theory is not in its complexity, but in its ability to explain and predict.
约翰·霍普克罗夫特
计算机科学中理论与实践之间的相互作用是推动该领域前进的动力。
"The interplay between theory and practice in computer science is what drives the field forward."
桑杰夫·阿罗拉
理论洞察可以带来实际突破，弥合抽象思想与现实应用之间的差距。
"Theoretical insights can lead to practical breakthroughs, bridging the gap between abstract ideas and real-world applications."
桑杰夫·阿罗拉
复杂性理论告诉我们，并非所有问题都是平等的；有些问题本质上比其他问题更难。
"Complexity theory teaches us that not all problems are created equal; some are inherently harder than others."
桑杰夫·阿罗拉
理论计算机科学不仅仅是解决问题，更是理解计算本身的本质。
"Theoretical computer science is not just about solving problems, but about understanding the nature of computation itself."
桑杰夫·阿罗拉
计算学习理论中的一个关键见解是，学习问题的复杂性由假设空间的复杂性和可用数据的数量决定。
"A key insight in computational learning theory is that the complexity of a learning problem is determined by the complexity of the hypothesis space and the amount of data available."
莱斯利·瓦利安特
计算学习理论为理解机器学习算法的能力和局限性提供了一个数学框架。
"Computational learning theory provides a mathematical framework for understanding the capabilities and limitations of machine learning algorithms."
莱斯利·瓦利安特
高效算法的开发不仅仅是一个理论练习；它对我们的生活方式和工作方式有实际影响。
The development of efficient algorithms is not just a theoretical exercise; it has practical implications for the way we live and work.
迈克尔·拉宾
计算机科学中理论与实践之间的相互作用是推动创新和进步的动力。
The interplay between theory and practice in computer science is what drives innovation and progress.
安德鲁·姚
计算复杂性理论的发展向我们展示了并非所有问题都是平等的。
The development of computational complexity theory has shown us that not all problems are created equal.
安德鲁·姚
理论计算机科学的重要性在于它能够为实际应用提供基础。
The importance of theoretical computer science lies in its ability to provide a foundation for practical applications.
斯蒂芬·库克
计算理论不仅仅是关于解决问题，还涉及理解可计算性的极限。
The theory of computation is not just about solving problems, but also about understanding the limits of what can be computed.
斯蒂芬·库克
计算理论的美在于它能够将世界的复杂性抽象成可管理和可理解的模型。
The beauty of computational theory lies in its ability to abstract the complexities of the world into manageable and understandable models.
莱昂尼德·莱文
理论见解常常导致实际突破，弥合抽象思想与现实世界应用之间的差距。
"Theoretical insights often lead to practical breakthroughs, bridging the gap between abstract ideas and real-world applications."
桑杰夫·阿罗拉
在计算学习理论中，挑战不仅仅是学习，而是理解学习是如何可能的。
"In computational learning theory, the challenge is not just to learn, but to understand how learning is possible."
桑杰夫·阿罗拉
理论计算机科学不仅仅是解决问题；它是关于理解计算本身的本质。
"Theoretical computer science is not just about solving problems; it's about understanding the nature of computation itself."
桑杰夫·阿罗拉
学习算法的设计应同时受到理论见解和实践考虑的指导。
The design of learning algorithms should be guided by both theoretical insights and practical considerations.
莱斯利·瓦利安特
在计算学习理论中，我们试图理解从数据中学习的基本原理。
In computational learning theory, we seek to understand the fundamental principles that govern learning from data.
莱斯利·瓦利安特
计算理论的美在于其抽象和概括的能力，将具体问题转化为通用解决方案。
The beauty of computational theory lies in its ability to abstract and generalize, turning specific problems into universal solutions.
曼纽尔·布卢姆
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。
Every problem in NP can be reduced to the satisfiability problem, which is the cornerstone of computational complexity theory.
理查德·卡普
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