Graph theory has long provided a robust mathematical framework for investigating networks, relations and connectivity in both abstract and applied settings. Recent advances have markedly refined our ...

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 ...

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” – ...

A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach. 1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer ...

Complexity theory is a fundamental branch of theoretical computer science that categorises computational problems according to their inherent difficulty and the resources required to solve them. At ...

A major advance reveals deep connections between the classes of problems that computers can — and can’t — possibly do. At first glance, the big news coming out of this summer’s conference on the ...

Since the 1930s, the theory of computation has profoundly influenced philosophical thinking about topics such as the theory of the mind, the nature of mathematical knowledge and the prospect of ...