MathDB
Binary function from {0,1}^n

Source: Miklós Schweitzer 2018 P7

November 10, 2018
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Problem Statement

Describe all functions f:{0,1}n{0,1}f: \{ 0,1\}^n \to \{ 0,1\} which satisfy the equation \begin{align*} & f(f(a_{11},a_{12},\dotsc ,a_{1n}),f(a_{21},a_{22},\dotsc ,a_{2n}),\dotsc ,f(a_{n1},a_{n2},\dotsc ,a_{nn}))\\ & = f(f(a_{11},a_{21},\dotsc ,a_{n1}),f(a_{12},a_{22},\dotsc ,a_{n2}),\dotsc ,f(a_{1n},a_{2n},\dotsc ,a_{nn}))\end{align*} for arbitrary aij{0,1}a_{ij}\in \{ 0,1\} where i,j{1,2,,n}.i,j\in \{1,2,\dotsc ,n\}.