Building-Block Identification by Simultaneity Matrix

Abstract

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