Algorithm for “safety” decomposition of the formal context

The $\#$P-complete problem of finding all formal concepts of a given formal context is investigated. An algorithm which we propose, allows in practice to solve this problem in a polynomial time. This algorithm is based on the method of “safety” decomposition of the formal context into parts called boxes. With “safety” decomposition of a formal context into boxes, no formal concept of the original context is lost and no new formal concepts arise. The decomposition process is aimed at consistently reducing the size of the boxes of the formal context and is implemented iteratively. The rules for stopping the process of decomposition of the formal context into boxes, which guarantee the polynomial time of the entire decomposition process, are established: setting the threshold value for the density of boxes and the number of iterations of the decomposition.