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Finding out whether a question is too difficult to ever solve efficiently depends on figuring out just how hard it is. Researchers have now shown how to do that for a major class of problems.

Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

For years, intermediate measurements made it hard to quantify the complexity of quantum algorithms. New work establishes that those measurements aren’t necessary after all.

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.

A recent paper set the fastest record for multiplying two matrices. But it also marks the end of the line for a method researchers have relied on for decades to make improvements.

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

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