Building-Block Identification by Simultaneity Matrix

We propose a BB identification by simultaneity matrix (BISM) algorithm. The input is a set of -bit solutions denoted by S. The number of solutions is denoted by n = |S|. The output is a partition of bit positions {0, . . . , − 1}. The BISM is composed of Simultaneity-Matrix-Construction and Fine-Valid-Partition algorithms. Algorithm SMC is outlined as follows (aij denotes the matrix element at row i and column j, Count S (i, j) = |{x ∈ {0, . . . , n− 1} : sx[i] = a and sx[j] = b}| for all (i, j) ∈ {0, . . . , − 1}2, (a, b) ∈ {0, 1}2, sx[i] denotes the i bit of x solution, Random(0,1) gives a real random number between 0 and 1).