The concept of a Turing machine is foundational to our understanding of computation.
图灵机的概念是我们理解计算的基础。
The future of computing lies in the integration of different fields, such as biology, physics, and mathematics.
计算的未来在于不同领域的整合，如生物学、物理学和数学。
The power of abstraction is crucial in computer science, allowing us to focus on the essential aspects of a problem.
抽象的力量在计算机科学中至关重要，它使我们能够专注于问题的本质方面。
The development of algorithms is both an art and a science.
算法的发展既是一门艺术，也是一门科学。
The theory of computation is deeply connected to the philosophy of mind and the nature of intelligence.
计算理论与心智哲学和智能的本质有着深刻的联系。
The study of computational complexity is not just about solving problems, but also about understanding the limits of what can be computed.
计算复杂性的研究不仅仅是关于解决问题，还在于理解可计算性的极限。
The concept of NP-completeness has provided a powerful tool for understanding the complexity of problems.
NP完全性的概念为理解问题的复杂性提供了一个强大的工具。
A problem is in P if it can be solved quickly by a computer, and in NP if a solution can be verified quickly.
一个问题如果在计算机上可以快速解决，那么它属于P类问题；如果一个解可以快速验证，那么它属于NP类问题。
The essence of computation lies in the transformation of information.
The importance of theoretical computer science lies in its ability to provide a foundation for practical applications.