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.

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 ...

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?

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 ...

They have a mathematical, analog “solver” that can potentially find the best solution to NP-hard problems. NP-hardness is a theory of computational complexity, with problems that are famous for their ...