Difference between revisions of "Address"
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Let <math>n = k + 2^k</math>. A function <math>f:\{-1,1\}^n \to \{-1,1\}</math> is called an '''address function''' if it returns the bit pointed to by the first <math>k</math> bits: | Let <math>n = k + 2^k</math>. A function <math>f:\{-1,1\}^n \to \{-1,1\}</math> is called an '''address function''' if it returns the bit pointed to by the first <math>k</math> bits: | ||
| − | <math>f(x_1, \ldots, x_k, y_1,\ldots,y_{2^k}) = y_{\tilde{x}}, </math> | + | :::{| class="wikitable" |
| + | |- | ||
| + | |<math>f(x_1, \ldots, x_k, y_1,\ldots,y_{2^k}) = y_{\tilde{x}}, </math> | ||
| + | |} | ||
| − | where <math>\tilde{x}</math> is number whose binary representation of the vector <math>(x_1,\ldots, x_k)</math>. | + | where <math>\tilde{x}</math> is number whose binary representation of the vector <math>(x_1,\ldots, x_k)</math>. |
== Properties == | == Properties == | ||
Revision as of 13:37, 20 November 2019
Definition
Let [math]n = k + 2^k[/math]. A function [math]f:\{-1,1\}^n \to \{-1,1\}[/math] is called an address function if it returns the bit pointed to by the first [math]k[/math] bits:
[math]f(x_1, \ldots, x_k, y_1,\ldots,y_{2^k}) = y_{\tilde{x}}, [/math]
where [math]\tilde{x}[/math] is number whose binary representation of the vector [math](x_1,\ldots, x_k)[/math].
Properties
- Please add some properties! Start off with relation to Juntas.
