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- Q5157642 subject Q7132792.
- Q5157642 subject Q7139268.
- Q5157642 subject Q7451559.
- Q5157642 subject Q7451729.
- Q5157642 subject Q9245233.
- Q5157642 abstract "In mathematics, the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set, the permanent weights them all with a +1 sign.While the determinant can be computed in polynomial time by Gaussian elimination, the permanent cannot. In computational complexity theory, a theorem of Valiant states that computing permanents is #P-hard, and even #P-complete for matrices in which all entries are 0 or 1.Valiant (1979) This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP. It is known that computing the permanent is impossible for logspace-uniform ACC0 circuits.(Allender & Gore 1994)The development of both exact and approximate algorithms for computing the permanent of a matrix is an active area of research.".
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- Q5157642 comment "In mathematics, the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns.".
- Q5157642 label "Computing the permanent".