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 ...

Lance Fortnow on the current status and future outlook of solving the P-NP problem.

Constraint satisfaction problems (CSPs) provide a versatile framework for modelling complex decision-making tasks where a collection of variables must be allocated values that satisfy specific ...

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 ...

Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently ...

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 ...

In the last few years, a few dedicated mathematicians have begun to study the computational complexity of video games. Their goal is to determine the inherent difficulty of the games and how they ...

Quantum computers get a lot of people excited because they solve problems in a manner that’s fundamentally different from existing hardware. A certain class of mathematical problems, called ...