How to solve the equation of binary logic operation, where all unknowns are 0 or 1

1 次查看（过去 30 天）

dcydhb dcydhb 2020-8-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/576805-how-to-solve-the-equation-of-binary-logic-operation-where-all-unknowns-are-0-or-1

编辑： dcydhb dcydhb 2020-8-8

equations.txt

For example, I have the following equations, linear equations and nonlinear equations, in which the unknowns can only take 0 or 1, and it is based on this operation rule,

for Addition operation：

1+1=0，1+0=1，0+1=1，0+0=0，

For multiplication operation：

0*0=0，0*1=0，1*0=0，1*1=1

so how to solve the values of all unknowns?

x1+x2+x3+(x4+1)*(x5+x6+1)=x1*x2, 
x2+x3+x4+(x5+1)*(x6+x1+1)=x2*x3, 
x3+x4+x5+(x6+1)*(x1+x2+1)=x3*x4, 
x4+x5+x6+(x1+1)*(x2+x3+1)=x4*x5, 
x5+x6+x1+(x2+1)*(x3+x4+1)=x5*x6, 
x6+x1+x2+(x3+1)*(x4+x5+1)=x6*x1, 

and in fact, the original question consists of 416 equations and 416 variables including form

c0...c31 and x1...x384 which should be only 0 or 1

as i have attached in the

equations.txt

6 个评论
显示 4更早的评论隐藏 4更早的评论

dcydhb dcydhb 2020-8-8

在 MATLAB Online 中打开

i want to say that the equation i have posted is just an example equation and my original equation consists of 300 unknowns so

i need other way rahher than brute force search.

Walter Roberson 2020-8-8

https://www.mathworks.com/help/comm/ref/gf.html

gf(x,1) appears to implement the required mathematics.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Bruno Luong 2020-8-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/576805-how-to-solve-the-equation-of-binary-logic-operation-where-all-unknowns-are-0-or-1#answer_476851

编辑：Bruno Luong 2020-8-8

在 MATLAB Online 中打开

[x1,x2,x3,x4,x5,x6]=ndgrid(0:1);
x1 = x1(:);
x2 = x2(:);
x3 = x3(:);
x4 = x4(:);
x5 = x5(:);
x6 = x6(:);
b = [x1+x2+x3+(x4+1).*(x5+x6+1)-x1.*x2, ...
x2+x3+x4+(x5+1).*(x6+x1+1)-x2.*x3, ...
x3+x4+x5+(x6+1).*(x1+x2+1)-x3.*x4, ...
x4+x5+x6+(x1+1).*(x2+x3+1)-x4.*x5, ...
x5+x6+x1+(x2+1).*(x3+x4+1)-x5.*x6, ...
x6+x1+x2+(x3+1).*(x4+x5+1)-x6.*x1 ];
b=mod(b,2);
idx = find(all(b==0,2));
for i=1:length(idx)
    k=idx(i);
    fprintf('x1=%d,x2=%d,x3=%d,x4=%d,x5=%d,x6=%d\n', x1(k), x2(k), x3(k), x4(k), x5(k), x6(k));
end

Result

x1=1,x2=0,x3=0,x4=0,x5=0,x6=0
x1=0,x2=1,x3=0,x4=0,x5=0,x6=0
x1=0,x2=0,x3=1,x4=0,x5=0,x6=0
x1=0,x2=0,x3=0,x4=1,x5=0,x6=0
x1=0,x2=0,x3=0,x4=0,x5=1,x6=0
x1=0,x2=0,x3=0,x4=0,x5=0,x6=1
x1=1,x2=1,x3=1,x4=1,x5=1,x6=1

mathematically, your systems are non-linear, since they have functions of variables being multiplied by functions of variables. In what you posted, the maximum degree is 2, which makes the system "quadratic", and there are techniques for dealing with quadratic functions. Does this extend in general to your equations, that you never "and" more than two variables together ?

dcydhb dcydhb 2020-8-8

i am sorry what does your 'and' mean, i have just attached the original equations and i think may you can just explore the original equations and thanks a lot!

请先登录，再进行评论。

请先登录，再回答此问题。