In computational complexity theory, P and NP are two classes of problems. P is the class of decision problems that a deterministic Turing machine can solve in polynomial time. In useful terms, any ...

The axiomatic treatment of the computational complexity of partial recursive functions initiated by Blum is extended to relatively computable functions (as computed, for example, by Turing machines ...

MIP * = RE is not a typo. It is a groundbreaking discovery and the catchy title of a recent paper in the field of quantum complexity theory. Complexity theory is a zoo of “complexity classes” – ...

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape. How fundamentally difficult is a problem?

Kolmogorov complexity uses computer science to measure the amount of information (or randomness) contained in finite objects. In addition to being interesting philosophically, Kolmogorov complexity ...

One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling discovery about the relationship between time and memory in computing.

Many aspects of modern applied research rely on a crucial algorithm called gradient descent. This is a procedure generally used for finding the largest or smallest values of a particular mathematical ...