Any ideas on how to solve a system of boolean equations with XOR(+) and AND(*) operations, that can contain x[i] AND x[j] (2nd degree), but not x[i] AND x[j] AND x[k] (i.e. no 3rd and above degree)?
More formally the system is like the following (all equations must be true simultaneously):
x[1] + x[2]*x[3] + x[3] + x[4]*x[5] = b[1]
x[1]*x[2] + x[3]*x[4] + x[5] = b[2]
... etc ...
Here b[i] is either 0 or 1. Of course, in the solution x[i] is also 0 or 1 (it's all boolean).