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Welcome to the Communication-Complexity Garden, the botanical companion to the Communication-Complexity Zoo. This field guide lists rigorously defined functions.


Gardeners: Florian Speelman and Christian Schaffner

To create a new problem, click on the edit link of the problem before or after the one that you want to add and copy the format, and save.


Table of Contents

2-party functions: Equality - Index -

Uncategorized problems: Index -


The Problems

Discrete Logarithm: Reverse exponentiation
Equality: Are two strings equal?

If Alice has a string Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x\in\left\{0,1\right\}^n} and Bob has a string Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\in\left\{0,1\right\}^n} , define EQUALITY(x, y) = 1 if and only if x = y.

Algorithms: ?

Memberships:


Index: What is the bit of x with index i?

Alice has a string Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x\in\left\{0,1\right\}^n} , Bob holds input Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i\in [n]} . Define INDEX(x,i)=x_i

Algorithms: ?

Memberships: ∈ NPcoAM.