I'm wondering about systems of equations that take on a finite set of values for those variables. Is there a theory behind that? In particular, solving systems where the variable takes on values of either 0 or 1. The problem is probably NP-hard, but I'm wondering where to look to learn more about it.
Like for example,
$a^2 + bc - a = 0$
$b(a + d) - b = 0$
$c(a + d) - c = 0$
$d^2 + bc - d = 0$ where a, b, c, d are from {0, 1}.