LLL-solver

In this paper we overview the possible way to solve for the “reasonable time” the NP-complete problems representatives called LLL-solver. This way is linked to the knapsack problem solving method offered by Lagarias and Odlyzko. Proved: the existence of such polynomial transformation of the 3-SAT problem to the knapsack problem that the image of the 3-SAT problem is situated in the area of knapsack with the density $d<C$, where $C$ is any given constant less or equal than $3(\log_27)^{-1}$. Introduced: the notion of the algorithm validity function. Showed: the results of the computer experiments on the calculation of the LLL-solver validity functions.