Computational complexity theory examines the intrinsic difficulty of algorithmic problems by classifying them into hierarchies according to the resources—typically time and space—required for their ...

Computability theory establishes which problems can in principle be solved by mechanical procedures, formalised by the Turing machine model and its equivalents. It draws a firm boundary between ...

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” – ...

The original version of this story appeared in Quanta Magazine. One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling ...