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 ...

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 ...

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

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?

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 ...

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 ...

The historical pursuit of creating intelligent machines has culminated in the modern era of artificial intelligence. However, the efficacy of AI applications is contingent upon a nuanced understanding ...

An Italian researcher with a penchant for retro games -- or perhaps just looking for an excuse to play games in the name of science! -- has used computational complexity theory to decide, once and for ...