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I have a set of boolean equations, i.e.

var1 = x AND y
var2 = x OR z
var3 = ...
var4 = ...

And the constraint that every output vari should equal 1.

I want every corresponding combination of input variables (x, y ,z ...) which satisfies these equations.

For example, the first two equations would allow [x y z] = [1 1 0] or [1 1 1] as solutions.

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1 回答 1

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如果你没有太多变量，你可以很容易地做到这一点。

如果您确实有很多变量，此方法将停止运行，因为它使用 size 的矩阵K*(2^K)，其中K是变量的数量，并且combvec对于较大的变量也很慢K。

虽然您必须警惕变量的数量，但这种方法非常有能力以很少的开销处理许多逻辑“方程式”。

在x, y,z示例中：

% Get all combinations of x/y/z, where each is true or false
opts = repmat( {[true, false]}, 1, 3 );
xyz = combvec( opts{:} )
% Assign each row to a named variable 
x = xyz(1,:); y = xyz(2,:); z = xyz(3,:);
% Get the combinations which satisfy your conditions
results = xyz( :, (x & y) & (x | z) );
% Each column of results is a solution
>> results
results = 
    1    1
    1    1
    1    0

写得更笼统，它可能看起来像这样：

K = 3; % K variables (previously x, y and z so K = 3)
% Create all true/false combinations
opts = repmat( {[true, false]}, 1, K );
combs = combvec( opts{:} );

% Shorthand so we can write in(i) not combs(i,:)
in = @(k) combs(k,:); 
% Apply conditions
results = combs( :, (in(1) & in(2)) ...
                  & (in(1) | in(3)) );

注意：如果您没有神经网络工具箱，您将没有combvec. 获得所有组合有很多选择。

于 2019-02-18T16:17:57.333 回答