We develop a polynomial-time algorithm to minimize pseudo-Boolean functions . The computational complexity is O\left( n^{15{2}}\right) , although very conservative, it is sufficient to prove that this minimization problem is in the  class P. A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O%DIFDELCMD < \left( %%% n^{\frac{45{2}}}%DIFDELCMD < \right) %%%  . The algorithm was implemented in MATLAB and checked by generating one million matrices of arbitrary dimension up to 24 with random entries in the range \left[ -50,50\right] . All the experiments were successful .
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs . The computational complexity is O\left( n^{15{2}}\right) , although very conservative, it is sufficient to prove that this minimization problem is in the complexity class P. %DIFDELCMD < \left( %%% {2}}}%DIFDELCMD < \right) %%% The implementation aspects are also described in detail with a special emphasis on the transformation of the quadratic program into a linear program that can be solved in polynomial time . The algorithm was implemented in MATLAB and checked by generating five million matrices of arbitrary dimensions up to 30 with random entries in the range \left[ -50,50\right] . All the experiments carried out have revealed that the method works correctly .
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We develop a polynomial-time algorithm to minimize pseudo-Boolean functions
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs
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complexity
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A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O
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n^{\frac{45
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The implementation aspects are also described in detail with a special emphasis on the transformation of the quadratic program into a linear program that can be solved in polynomial time
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one
five
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dimension up to 24
dimensions up to 30
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were successful
carried out have revealed that the method works correctly