Decades-Old Computer Science Conjecture Solved in Two Pages

https://www.quantamagazine.org/mathematician-solves-computer-science-conjecture-in-two-pages-20190725/ [www.quantamagazine.org]

2019-07-26 03:04

“This conjecture has stood as one of the most frustrating and embarrassing open problems in all of combinatorics and theoretical computer science,” wrote Scott Aaronson of the University of Texas, Austin, in a blog post. “The list of people who tried to solve it and failed is like a who’s who of discrete math and theoretical computer science,” he added in an email.

Over the years, computer scientists have developed many ways to measure the complexity of a given Boolean function. Each measure captures a different aspect of how the information in the input string determines the output bit. For instance, the “sensitivity” of a Boolean function tracks, roughly speaking, the likelihood that flipping a single input bit will alter the output bit. And “query complexity” calculates how many input bits you have to ask about before you can be sure of the output.

Also: https://www.scottaaronson.com/blog/?p=4229

Paper: https://arxiv.org/abs/1907.00847

Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture