Assume that $A=\{a\_{ij}\}$ is an $M\times N$ matrix where $M<N$ and $Ax=b$ where $x$ is the vector of unknown variables and $b$ is a known binary vector. Assume $a\_{ij}$ values are also binary. Clearly $Rank(A)\le M$, so the number of variables is larger than the number of equations. However, still some of the variables might be calculated (or maybe not, it depends on $A$). I am looking for a systematic algorithm to find all variables that can be calculated in the existing under-determined system.