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Miklós Schweitzer
2018 Miklós Schweitzer
7
7
Part of
2018 Miklós Schweitzer
Problems
(1)
Binary function from {0,1}^n
Source: Miklós Schweitzer 2018 P7
11/10/2018
Describe all functions
f
:
{
0
,
1
}
n
→
{
0
,
1
}
f: \{ 0,1\}^n \to \{ 0,1\}
f
:
{
0
,
1
}
n
→
{
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
a
i
j
∈
{
0
,
1
}
a_{ij}\in \{ 0,1\}
a
ij
∈
{
0
,
1
}
where
i
,
j
∈
{
1
,
2
,
…
,
n
}
.
i,j\in \{1,2,\dotsc ,n\}.
i
,
j
∈
{
1
,
2
,
…
,
n
}
.
function
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