---
title: "On the Communication Complexity of Equality"
description: "These are some quick sketchnotes based on this lecture by Ryan O’Donnell, a part of the playlist for the awesome CS Theory Toolkit course. You can walk through the arguments bel..."
pubDate: "2021-10-04"
authorName: "Neeldhara"
sourceCategories: ["sketchnotes", "lecturenotes"]
sourcePath: "communication-complexity-equality/index.qmd"
---

These are some quick sketchnotes based on  [this lecture](https://www.youtube.com/watch?v=orOJRhlqrvk) by [Ryan O’Donnell](https://www.cs.cmu.edu/~odonnell/), a part of the  [playlist](https://www.youtube.com/watch?v=prI35GmCon4&list=PLm3J0oaFux3ZYpFLwwrlv_EHH9wtH6pnX) for the awesome [CS Theory Toolkit](https://www.diderot.one/course/28/) course. You can walk through the arguments below.

<iframe src="https://slides.com/neeldhara/deck-85ae95/embed?style=transparent&byline=hidden" width="795" height="420" title="Communication Complexity of Equality" scrolling="no" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>

I should mention that while the [Schwartz-Zippel-DeMillo-Lipton lemma](https://rjlipton.wpcomstaging.com/2009/11/30/the-curious-history-of-the-schwartz-zippel-lemma/) is invoked in the notes below, one could make do with just the fact that over any field $F$, any degree $n$ polynomial has at most $n$ roots, as pointed out by [@dsivakumar](https://twitter.com/dsivakumar) — thanks!

<blockquote class="twitter-tweet"><p lang="en" dir="ltr">In the fourth slide from the end, why [DeMillo--Lipton]--Schwartz--Zippel Lemma? You only need that number of roots of a polynomial (over Z mod q) of degree n is no more than n. You don&#39;t need D-L/S/Z, which gives a general version for multivariate polynomials, right?</p>&mdash; D. Sivakumar (@dsivakumar) <a href="https://twitter.com/dsivakumar/status/1269351801108623360?ref_src=twsrc%5Etfw">June 6, 2020</a></blockquote>
