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The power of randomness in algorithms is that it can help us find solutions that are difficult to discover through deterministic methods.
In quantum mechanics, the act of measurement can change the state of the system being measured.
"We need to think of software not just as code, but as a mathematical object that can be analyzed and verified."
Every problem in NP can be reduced to the satisfiability problem, which is the cornerstone of computational complexity theory.
The essence of computational complexity is to understand the limits of what can be computed efficiently.
The Internet is a place where people can connect, share, and learn.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
I can accept failure, everyone fails at something. But I can't accept not trying.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
Mathematics is the language of the universe, and through it, we can understand the fundamental principles that govern our world.
The challenge of quantum computing is not just in building the hardware, but in understanding the new algorithms that can take advantage of it.
The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.
Any problem in computer science can be solved with another layer of indirection.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
The theory of computation provides a foundation for understanding what can and cannot be computed.
Program testing can be used to show the presence of bugs, but never to show their absence!
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
The original idea of the web was that it should be a collaborative space where you can communicate through sharing information.
The Liskov Substitution Principle is a fundamental concept in object-oriented programming, ensuring that derived classes can be used in place of their base classes without altering the correctness of the program.