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# computational complexity

## Latest Articles

### Alan Turing and the Power of Negative Thinking

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

### Complexity Theory’s 50-Year Journey to the Limits of Knowledge

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

### To Move Fast, Quantum Maze Solvers Must Forget the Past

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.

### How to Build a Big Prime Number

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

### Computer Scientists Inch Closer to Major Algorithmic Goal

A new paper finds a faster method for determining when two mathematical groups are the same.

### Mathematicians Complete Quest to Build ‘Spherical Cubes’

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

### The Computer Scientist Who Finds Life Lessons in Games

In Shang-Hua Teng’s work, theoretical and practical questions have long been intertwined. Now he’s turning his focus to the impractical.

### New Algorithm Closes Quantum Supremacy Window

Random circuit sampling, a popular technique for showing the power of quantum computers, doesn’t scale up if errors go unchecked.

### The Year in Computer Science

Computer scientists this year learned how to transmit perfect secrets, why transformers seem so good at everything, and how to improve on decades-old algorithms (with a little help from AI).