Understanding the Communication Complexity of Equality | CMU Lecture 10d 📚

Every nonzero degree-d polynomial has at most d roots. A very simple fact, but what is it good for? One application is to the communication complexity of Equality. Suppose Alice and Bob have n-bit strings. How many bits do they need to communicate to know whether or not their strings are equal? The answer may surprise you: just O(log n), if you allow a tiny probability of error. Lecture 10d of "CS Theory Toolkit": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University. Resources for this lecture: . "A computational introduction to number theory and algebra", by Shoup . Forney course 6.451 notes, chapter 7, "Introduction to finite fields" Taught by Ryan O'Donnell (https://www.cs.cmu.edu/~odonnell) Course homepage on CMU's Diderot system: https://www.diderot.one/course/28/ Filmed by Cole H. for Panopto (http://www.panopto.com/) Thumbnail photo by Rebecca Kiger (https://www.rebeccakphoto.com/)