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# Computational complexity

## Latest Articles

### ‘Magical’ Error Correction Scheme Proved Inherently Inefficient

Locally correctable codes need barely any information to fix errors, but they’re extremely long. Now we know that the simplest versions can’t get any shorter.

### The Year in Computer Science

Artificial intelligence learned how to generate text and art better than ever before, while computer scientists developed algorithms that solved long-standing problems.

### An Easy-Sounding Problem Yields Numbers Too Big for Our Universe

Researchers prove that navigating certain systems of vectors is among the most complex computational problems.

### 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.